Start as America because they are the strongest country and close to central America. Take over the countries you would normally in a 10 countries run, the order doesn't really matter but the Bahamas and Haiti should work. Then after you take those two you'll want to do the trade deal good times and sell about 50 items to get you about 5000 gold. Make sure to explore countries around where ever you're trading. The 5000 gold will allow you to sweep the central American countries and the islands. Also make sure to always get planes, they become less important later on but they give you a big boost in gold.

Now you basically enter a phase where you find every country that has an army of 10 and sometimes a navy of 10 too. You'll need to find them and take them over. You should move your army to your Americas Base and take over Iceland while you're there then take over the weak nations of western Africa while avoid anyone who has over 10 in their military. Make sure to max their economy out when after you take them over. You want to trade for as much money as you can because at the end of the run its going to make or break the run.

Another thing is nukes, make sure to only nuke major countries that have almost full armies, it will help you from going bankrupt from the price of a maxed out army. Which is also why you should save up as much money as you can because you wont have enough nukes for all of the majors. Also never nuke the UK it's a waste, or if you do make sure you took all their colonies before you do because when a colonizer is taken over, ALL of their colonies are released as usually really strong countries. Its best just to use a nuke that was meant for the United Kingdom on someone else.

After you take the weaker countries out you're going to move onto taking countries that have 41 in their army and countries who have 34 in their army and 32 in their air force. Something that should really help you is setting your buy amount for the army and air force to 50 because it give you 2.5 or so which can give you 32 after the first 30 or hit it twice for 34 after getting the first 30. I know it sounds weird but trust me you'll understand if you do a run. (maybe)

Then you enter what is essentially a third phase where you start taking the stronger countries, like Norway or Sweden. Soon most countries that aren't majors will be gone. Also I recommend nuking Mexico and Brazil and then taking them in this stage so you can focus on Europe and go right into Asia instead of running back and forth between Asian all the way to the Americas in the last part of the run. Now comes the part where you take out every country you nuked into being weaker, while you're taking them over you should make sure to trade for as much gold as you can because you're going to need it. After you take them out you will be forced to take on the majors and after they're gone you've finished your 159 countries Speedrun.

This is move of an outline than a guide, "its less of do this and then do this" because a lot of it is doing the same general thing for 30 minutes.