'Fear the Repo' - 'Waking Up the Neighbors' chain and 3× 'O, Brothel, Where Art Thou?' (00:17:43 - 00:29:00)
om0 'Waking Up the Neighbors' skips a mission from the highest unlocked strand. In the current route this is Louise: 'When Funday Comes'. The out-of-bounds strat only works in PSP versions.
3× 'O, Brothel, Where Art Thou?' skips 2 missions from the highest unlocked strand. In the current route this is Louise: 'Takin' Out the White-Trash' and 'D.I.V.O.R.C.E.'. This allows for early completion of 'To Victor, the Spoils'.

2× 'Got Protection?' (00:31:48 - 00:35:33)
Skips a mission from the highest unlocked strand. In the current route this is Phil: 'Boomshine Blowout'. Tested and confirmed on every version.

'Taxi Driver' instapass (International PSP only) [found by Powdinet]
You need to save and quit within ~5 seconds or the game crashes.

'Vigilante' triple and fail (PSP)
1) Start tripled 'Vigilante' --> counter: 3
2) Complete level --> counter: 6
3) Cancel once --> counter gone
4) Start after 2nd set of criminals spawn --> counter: 9
5) Complete level --> counter: 12
6) Cancel once --> counter gone
7) Start after 2nd set of crimanls spawn --> counter: 15
Cancel once --> Mission passed

The setup can be combined with "destroy vehicle" Rampages.

'Air Rescue' with Hunter [found by RationalPsycho]
Description by Momo_Ouali2001:
Fly to Sunshine Autos, then start Vigilante and cancel it while picking up one of the padlocks. You have now gained control of Vic while also having the option to buy a vehicle. Hold X Throughout the whole thing (If you want to get out of a vehicle in this state, Hold Triangle, then release X, then hold X and release Triangle). Now start om0 rampage 1, then fly to the Beach Patrol BF Injection, get out of the Hunter, get in the BF Injection and start Beach Patrol (You must start the Coastguard version) before the rampage ends. Now go to the Ocean Beach hospital, take the Air Ambulance and fly back to the beach. Now get on the Coastguard, then get back in the Air Ambulance. You now have a 30sec timer to get back in the Coastguard, once it reaches 1sec, start Air Rescue. Now, you're near the BF and Air Rescue is active, but the mission won't progress till you enter a vehicle. NOW release X to buy the vehicle you've been holding this entire time, and the game will warp you to Sunshine Autos, where the padlock you picked up was. Now RUN to the airport (DON't take any vehicles on the way, else you'll be doing Air Rescue with that vehicle) (use your Binoculars to megajump repeatedly instead of running normally, you'll save a few seconds that way.) and take the Hunter. As a result of all this, you're doing Air Rescue with a Hunter instead of the intended Air Ambulance!

2× 'Fire Fighter'

2× 'Truck Stop' (00:33:18 - 00:39:22)
Skips 'Marked Men' in the current route. Tested and confirmed on every version. Requires a save and quit after the dupe in International PSP versions, otherwise the 'Hose the Hoes' chain can crash.
This is a cutscene dupe so you can softlock or crash the game if you mess up the timing. You need to spam X to skip the first cinematic cutscene before it even appears. The first ingame cutscene will play, wait it out and the second cinematic cutscene will start. Skip the second cinematic cutscene after ~1 second. The second ingame cutscene will play which can be skipped anytime.
Regarding the truck, there are multiple outcomes:
A) Driving on its wheels: proceed as usual.
Stuck upside down: go out of bounds and unflip the Perennial then proceed as usual OR throw a grenade to them and get back in the Perennial before the truck blows up. The out-of-bounds strat only works in PSP versions.
C) Stuck on its side: drive the Perennial next to it so your gunners can shoot the enemies (fastest scenario).
D) Stuck on top of the fake truck: try to drive the fake truck out from underneath the real one. The real truck might flip to its side in this process.
E) The truck will blow up before you reach it. (uncommon)
F) The game will crash before you reach the truck. (rare)
In scenarios B, C and D Phil's truck can get stuck inside the fake truck on the way back, so the fake truck can be moved out of the way in advance for safety, which is heavily recommended for PPSSPP runs.

Comparison:

Grenade strat if truck is upside down:

This description and videos don't cover the recently discovered Partial Act Change Skip glitch.

'The Bum Deal' - 2× 'Snitch Hitch' - Hospital Asset chain (01:11:45 - 01:18:23)
Skips 'From Zero to Hero'. Only works in Japanese PSP and all PS2 versions.
Note that if you had done the 'Hose the Hoes' chain without save and quitting afterwards, the molotovs will be effective in a much smaller radius.
This is a cutscene dupe so you can softlock or crash the game if you mess up the timing. Skip the first cinematic cutscene when the rampage fails. The first ingame cutscene will play, wait it out and the second cinematic cutscene will start. Skip the second cinematic cutscene after ~1.5 seconds (when Lance says "No, blue."). The second ingame cutscene will play which can be skipped anytime.
Sometimes the two instances won't pass at the same time and 'From Zero to Hero' won't be skipped. There is no way to manipulate this with our current knowledge.
Wether the Hospital Asset gets bought immediately after the mission depends on when act change happens (storyline pager is a good indicator). If it's for sale buy it now and do the New Rocket Asset setup for 2× 'Turn on, Tune in, Bug out', otherwise do the original Rocket Asset (with this asset) setup for the dupe.

This description and video doesn't cover the recently discovered Partial Act Change Skip glitch.

Rocket Asset and 2× 'Turn on, Tune in, Bug out' w/ 30k Rockets
You can start and cancel 'Vigilante' during the om0 Rampage to disable gang spawns (optional but recommended for New Rocket Asset).
Cutscene dupe the mission to keep the Rocket Launcher with 30k ammo from the Rampage. If the player has more than 8 rockets, the Ammu-Nation objective is skipped. You can softlock or crash the game if you mess up the timing.
Original Rocket Asset setup (01:44:55 - 01:47:28)
Uses the Hospital Asset

New Rocket Asset setup
Uses the Asset behind the hotels on Ocean Drive (same one that Minigun Asset used)

You can also cutscene dupe a bunch of other Chapter 3 missions to obtain 30k ammo from Rampages.

2× 'Over the Top'
Skips Last Stand. Tested and confirmed on International and Japanese PSP.
See also: https://www.speedrun.com/gtavcs/thread/deoe1

2× 'Marked Men'
Skips a Phil mission. Useless since there aren't any more after 'Marked Men'.
This is a cutscene dupe so you can softlock or crash the game if you mess up the timing.

2× 'To Victor, the Spoils'
Skips a mission from the highest unlocked strand. Doesn't fit into the current route.
This is an "entrance dupe", similar to the first dupe when doing 3× 'O, Brothel, Where Art Thou?', although 'Vigilante' timer is not necessarily required.

2× 'Money for Nothing'
Skips 'Leap and Bound'. This allows for early completion of 'The Bum Deal', although it is still faster to do 'Caught as an Act' first.
Tested on confirmed on International and Japanese PSP versions.
This is a cutscene dupe so you can softlock or crash the game if you mess up the timing.
Unfortunately the timing here is so extremely precise, that as of this post we consider this dupe humanly impossible to pull off in a run.

2× 'Turismo'
Starting race A, then starting and finishing race B passes both races A and B (and gives % for both). Can be combined with any of the races.

2× 'Steal the Deal' (showcase with Cheat Engine)
Skips 'The Exchange'.
This is a cutscene dupe so you can softlock or crash the game if you mess up the timing.
You need to take the correct Lance and the correct Jet Ski with you in order to progress the mission. Use the mission instructions on the bottom of the screen as indicator.
This demonstration video uses Cheat Engine to teleport the boat to the final objective marker. Unfortunately, as of this post, we don't know of a way to complete the mission normally because the boat is invisible and has no physics.

3x Extortion
Tested in: International version (& might work on Japanese version)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 rampage. During om0, you'll notice that a pager will come out immidiately. If payday pager comes out, start vigilante again (/ spam vigilante tooltip by pressing rectangle while holding cross button) and cancel vigilante while getting into the empire.
(3) Start the first instances of Extortion, then go outside of empire building. You can either wait for the rampage to end while standing onto the next rampage (this will come in handy later on) or end the rampage faster by shooting the objective while standing onto the next rampage
(4) After the first rampage ends, the next rampage will start while a pager buffers in. The Story Pager itself will puts you back onto om0, letting you to start another instances of Extortion.
(5) While om0 rampage, start the second instances of Extortion, then finish the rampage (/ wait for the rampage to end). After that, start the third instances of Extortion.
(6) Good job! Now do the empire mission normally.

Notes:
- The first & second rampage needs to be different(?) (location wised)
- Keep in mind that Extortion (x3) is far more unstable than Extortion (x2), thus making the game more prone into crashing, as you can see from the videos below

3x Robbery (starts at Robbery #1)
Tested in: International version (& might work on Japanese version)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 rampage. During om0, you'll notice that a pager will come out immidiately. If payday pager comes out, start vigilante again (/ spam vigilante tooltip by pressing rectangle while holding cross button) and cancel vigilante while getting into the empire.
(3) Start the first instances of Robbery, then go outside of empire building. You can either wait for the rampage to end while standing onto the next rampage (this will come in handy later on) or end the rampage faster by shooting the objective while standing onto the next rampage
(4) After the first rampage ends, the next rampage will start while a pager buffers in. The Story Pager itself will puts you back onto om0, letting you to start another instances of Robbery.
(5) While om0 rampage, start the second instances of Robbery, then go outside of empire building to finish the rampage (/ wait for the rampage to end). After that, start the third instances of Robbery.
(6) Good job! Now do the empire mission normally.

Notes:
- The first & second rampage needs to be different(?) (location wised)
- On each instances of Robbery, YOU MUST GET OUT OF THE EMPIRE BUILDING otherwise the mission will fail due to "destroyed" vehicle
- Starting Robbery #1 thrice allow us to dupe Robbery #4 without skipping any major completion point, thus making the setup more consistent

3x Drugs (starts at Drugs #2)
Tested in: International version (& might work on Japanese version)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 rampage. During om0, you'll notice that a pager will come out immidiately. If payday pager comes out, start vigilante again (/ spam vigilante tooltip by pressing rectangle while holding cross button) and cancel vigilante while getting into the empire.
(3) Start the first instances of Drugs, then go outside of empire building & move the mission Esperanto away from the spawn point. You can either wait for the rampage to end while standing onto the next rampage (this will come in handy later on) or end the rampage faster by shooting the objective while standing onto the next rampage
(4) After the first rampage ends, the next rampage will start while a pager buffers in. The Story Pager itself will puts you back onto om0, letting you to start another instances of Drugs.
(5) While om0 rampage, start the second instances of Drugs, then go outside of empire building & move the mission Esperanto away from the spawn point. While doing so, finish the rampage (/ wait for the rampage to end). After that, start the third instances of Drugs.
(6) Good job! Now do the empire mission normally.

Notes:
- The first & second rampage needs to be different(?) (location wised)
- On each instances of Robbery, YOU MUST MOVE THE MISSION ESPERANTO AWAY FROM SPAWN POINT otherwise the mission will fail due to "destroyed" vehicle
- Starting Drugs #2 thrice will put us in a wierd spot. By doing so, we forced to do Drugs #5 (instead of duping Drugs #4), which is the worst Drugs mission of all.
- You can't do this setup on Drugs #1, since we required to get out of the empire upon doing so.

3x / 4x / 5x Turismo
Tested in: International version (& might work on Japanese version)

(only showcase the 3x ones. for 4x / 5x, just add one / two more pager on the setup, and you're good to go)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 rampage. During om0, you'll notice that a pager will come out immidiately. If payday pager comes out, start vigilante again (/ spam vigilante tooltip by pressing rectangle while holding cross button) and cancel vigilante while getting into the empire.
(3) Start the first Turismo (Race A). You can either wait for the rampage to end while standing onto the next rampage (this will come in handy later on) or end the rampage faster by shooting the objective while standing onto the next rampage
(4) After the first rampage ends, the next rampage will start while a pager buffers in. The Story Pager itself will puts you back onto om0, letting you to start another instances of Turismo.
(5) While om0 rampage, start the second Turismo (Race B ), then finish the rampage (/ wait for the rampage to end). After that, start the third Turismo (Race C).
(6) Good job! Now do the race normally (important note: you need to enter the race marker to start all three races).

Notes:
- The first & second rampage needs to be different(?) (location wised)
- Race A, B, C needs to be different (ex. Turismo #1, #2, & #3)

3x Time Trials (works on all Dirt Time Trials)
Tested in: PSP Japanese (& PS2 International ; confirmed by Momo_Ouali2001) (doesn't work on PSP International due to rampage placement)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 rampage. During om0, you'll notice that a pager will come out immidiately. If payday pager comes out, start vigilante again (/ spam vigilante tooltip by pressing rectangle while holding cross button) and cancel vigilante while getting into the empire.
(3) Start the first instances of Time Trials, then go to the designated Rampages (near Time Trials).
(4) After the first rampage ends, the next rampage will start while a pager buffers in. The Story Pager itself will puts you back onto om0, letting you to start another instances of Time Trials.
(5) While om0 rampage, start the second instances of Time Trials, then wait on the Time Trials menu. Start the course around 18 seconds before the rampage ended, this will prevent you to fail the second Time Trials due to "double clock" dismount time that's occuring. After bouncing back om0 (while on course of course), start the third instances of Time Trials.
(6) Good job! Now do the trials normally.

Notes:
- The first & second rampage needs to be different(?) (location wised)
- Due to no Taxi Instapasses, it's basically useless to run 100% on Japanese Version (unless we found a way to get the IP back onto the track of course..)

3x Time Trials (Works On All Dirt Time Trials) - Setup #1
Tested in: International / EU version (Finally! :3)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 rampage. During om0, you'll notice that a pager will come out immediately. If payday pager comes out, start vigilante again to hold the Story Pager on backlog.
(3) Pay attention to this section... When you arrive at Trials place (while still on rampage timer of course), cancel vigilante immediately and wait for the Story Pager to load in before starting any Time Trials. This will come in any of the two situation as follows:
> (Hard Mode) If the pager didn't come immediately after cancelling vigilante, start Time Trials EXACTLY 5 seconds after the first frame of pager shows up.
> (Easy Mode) If the pager comes immediately after cancelling vigilante, wait for roughly 2 seconds and then start Time Trials immediately.
Both interaction will puts you back om0, allows you to start one more instances of Time Trials.
(4) While still on om0 rampage, start the second instances of Time Trials, then wait on the Time Trials menu. Start the course around 18 seconds before the rampage ended, this will prevent you to fail the second Time Trials due to "double clock" dismount time that's occuring. After bouncing back om0 (while on course of course), start the third instances of Time Trials.
(5) Good job! Now do the trials normally.

Notes:
- On related note, here's a different take to the setup: https://discord.com/channels/139535251235012609/817081643373166625/851070873133514752
- You need to pay attention on step #3, otherwise you can fail this setup easily due to pager being loaded in immediately

3x Time Trials (Works On All Dirt Time Trials) - Setup #2
Tested in: International / EU version (Finally! :3)

Rundown:
(0) You must do the setup after 16:00 (/4 PM ; for Payday Pager) with 1 Story Pager on your backend (i recommend load the save before 16:00 to make sure that the Payday Pager will come out first instead of the Story Pager).
(1) Start an empire mission, go outside of empire building, and find a cop bike / cop car (cop bike is more preferable)
(2) Start Vigilante (this will cancel the empire mission as well) and do om0 padlock on Sunshine Autos. After that, start Vigilante IMMIDIATELY so that you stop any pager to load in.
(3) Go to any designated rampage (i recommend using the Molotov / police station AK-47 rampage) and start om0 rampage. During om0, you'll notice that a pager will come out immediately. If payday pager comes out, start vigilante again to hold Story Pager on backlog.
(4) When you arrive at Trials place (while still on rampage timer of course), cancel vigilante immediately and start the first instances of Time Trials. Immidiately after starting Time Trials, start mashing X (/ cross) button to warp you back to Sunshine Autos while still on Time Trials menu. When you already warp back, go to the second designated rampage before rampage timer ended (i recommend using the Pistol / Sniper Rifle rampage).
(4) Already on second designated rampage? good. While doing so, only start the 1st course when rampage timer goes 0 second on-screen. This action alone will warp you back onto Trials place while starting the first instances of Time Trials. Not only that, both rampage and pager will load in immediately thus putting you back om0 rampage again.
(5) While still on om0 rampage, start the second instances of Time Trials, then wait on the Time Trials menu. Start the course around 18 seconds before the rampage ended, this will prevent you to fail the second Time Trials due to "double clock" dismount time that's occuring. After bouncing back om0 (while on course of course), start the third instances of Time Trials.
(6) Good job! Now do the trials normally.

Notes:
- The setup itself were definitely slower than Setup #1, but it adds more consistenty into the mix, thus making this setup more approachable than Setup #1.
- When you get the Time Trials menu, you want to dismount yourself from Trials vehicle as soon as possible. You have two ways to do this:
a. By mashing triangle button while holding left/right to scroll the menu. This will put the menu on buffer while preventing you from getting out of the menu
b. By scrolling the menu first (either left / right), and then mash acceleration / X (/ cross) button to hit your vehicle onto any nearby walls

2× 'Accidents Will Happen'
Skips Kill Phil (as The Colonel's Coke is already skipped by PACB)
Works on INTL/JP PSP
Just spam X when the rampage timer disappears
Full setup video:

2× 'The Exchange' (Note: Obsoleted dupe - superseded by Diaz Skip - video soontm)
Skips Over the Top (with PACB done)
Works on INTL/JP PSP
Just spam X when the rampage timer disappears until the vans appear
Full setup video:

'Paramedic' instapass [found by Powdinet]
Confirmed to work on Int PSP.
1) Start "Purple Haze".
2) Drive into the water and start "Paramedic" in a way that it starts after it changes the camera to "drowning".
- If you start Paramedic without being fully in water, you crash.
- If you are fully in water before triggering it, you're softlocked.
3) Save and quit to get rid of stuck "Purple Haze" instance.