USNA Strategy
General Guide
If you are going to play as the USNA, on either Armageddon or the Abyss you've got a long game ahead of you. You'll be at war for the vast majority of the game, without enough preparation. In Abyss, you do not start immediately at war you'll have a little more time to prepare, but not nearly enough. Armageddon throws you straight into it, and trying to fight a World War with 1918 equipment. Hopefully with these tips you can try and win an equal world war.
Abyss
Research
This is going to be an extremely frustrating area. You start at a huge disadvantage compared to a normal game in terms of research of modern weaponry, techniques, and doctrines, starting with only the most basic technologies. On the plus side, you can pick whatever way you want to go, and your tech teams are all good, but none are extraordinary. Your land researcher, Omar Bradley, is best suited for the German Spearhead doctrine, so you should probably pick that. In terms of naval research, you are equally good at either Base Strike, or Fleet in Being, so that is your choice. However, you should probably not be worrying about naval research until you have stabilized your terrible ground situation. The first things that you should definitely research are Rear Area Supply Dumps, 1936 Infantry, your land doctrine of choice, probably Machine tools for the IC boost and whatever else you think you need without delay. You might want to research Improved Construction as soon as you can so you can start building Naval and Air bases too when you start conquering new territories. Secret weapons probably are not worth the effort because of how quickly the war starts, and how much IC will be taken up just trying to survive. Once you've made allies, trade blueprints with them of course. You will not be able to research everything, so pick an strategy for naval combat, air combat, and ground combat, and try and stick with it.
Resources
You do not have enough resources to run your industry even to begin with. You should immediately attempt to trade as much supplies as you can to get a bare minimum of war materials flowing in. Unfortunately everybody else is in pretty much the same position as you, so don't hold your breath. Building more factories is probably unnecessary; again you will probably be heading to war quickly.
Relationships
Try and build up friendly relations with all the democracies as quickly as possible. You are the leader of the allies, and if you don't bring them together, nothing will. Don't ally immediately unless you want to ensure that when one of your democratic allies declares war on somebody, or has war declared on them, you'll be drawn into it. You'll often see the AI players start declaring war on one another in January when the game is set to Furious, so usually by the time you build up good enough relationships to ensure alliances they will already be at war. Only build up relationships with countries you are not going to ally with if you are feeling particularly generous or need resources from them. You will be at war with them rather quickly anyway. Signing non-aggression pacts is a great way to delay war for you, but if you do you will have to sign it with every non-democracy. All can, and probably will, declare war on you. If you do this however, you'll be leaving your allies in the cold, probably leading to their collapse if you do not intervene quickly.
Spying
No AI player will ever use the intelligence system, so if you want to ignore it go ahead. It can be worthwhile to build up spies to gain info about the other country's army, but unless you want to spend a lot of time and money on other operations, it's probably not worth it.
Sliders and Ministers
You start with good sliders in some ways, but they are crappy in their own way. Everything except democracy and interventionism are in the middle. You only get the yearly change to definitly change your sliders, and while you might get random events to change your policy but don't count on it, so you are going to have to decide what is most important you change first. Ministers are all very good, it's your choice about what you want to focus on and who to choose, and when.
Armed Forces
War will start early. Therefore, as soon as your 1936 infantry research has finished start a big run of those guys. Organize your navy and air force as you see fit, but they will basically be useless to deciding things in the short to medium term. If you do want them to be decisive you are going to have to do a ton of research in those fields and a ton of construction. Your navy is definitely your second most important branch, but it will take too long to build a respectable force unless you manage to worm your way out of war for two years or more. You should probably disband your subs, but not your whole fleet. If you want to try building a few more vessels to ensure numerical superiority, go ahead, nobody else will even try to build up their navy. Your first enemy will be the Confederates and they own the Caribbean, and you'll need something to secure your transports as you take their victory point islands. Naval forces are also very helpful against the Liberatores in South America where big, poorly traversable, heavily defended provinces make land attack almost impossible, and landings can make a huge difference in distracting them long enough for your main forces to punch through. Air forces can always aid, but you will probably not have enough spare IC in the short term to build something respectable, and the enemy's force is as weak as yours, so defending against it will not be particularly difficult or life and death either. Infrastructure is good throughout the map, even in Africa, Asia, South America where in a normal game the infrastructure is normally very poor, so tanks can be used almost anywhere, so save up and buy them when you have enough spare IC, and good enough tanks researched.
Other Notes
You'll need a lot of transports if you want to fight in Eurasia, which you probably will have to if you want to keep your allies from collapsing, particularly China, which has enemies on all sides, or to finish off Africa, where the large provinces make it difficult for the AI players to manage conquering, on top of your ally in Africa having to deal with his main provinces in Europe being under attack by three different countries. Generally, however, you can relax after the Confederates and, to a lesser extent, the Liberatores, have been crushed, take the time to build up your forces, watch the world slowly fight itself into exhaustion, then send your forces in where you want, and conquer huge swaths of territory, which you then have to garrison and occupy. This can be really fun game, much like playing the United States in a regular game, but with more powerful allies.