^If you are lucky, the CS army will be a paper tiger, as sometimes happens with the American factions. Otherwise you will be fighting what is probably the strongest individual nation in the game. Try and encircle and destroy some divisions early on in places like Quebec and Florida, don't get bogged down in the Appalachians. Airpower is probably going to be your greatest asset, I don't think the CSA ai is big on building aircraft. If you aren't already at war with the CSA then consider taking Mexico first to use as a staging area and spread the Americans out. Use amphibious invasions to keep multiple front's open (you will probably want a staging area closer to NA), you can handle multiple fronts way better than the ai can. Lastly, if you are part of Mittleuropa or otherwise have access to Pacific bases, consider landing in Cali/British Columbia that should really make the ay's life a living hell.
Well the AUS is the clear loser, they are behind in resources, industry, and manpower, will likely have the most trouble behind friendly lines (blacks) and the least foreign support. The reds have the bulk of the industry but not all of the natural resources to fuel that industry (I'm not an expert on the involved supply chains, but I suspect they would have trouble getting the material for, say, aircraft). They also will lack oil, meaning that they will have trouble keeping aircraft and vehicles in the field. They have only one real point of entry for supplies (NYC) and it's dangerously exposed to Federal troops and especially Federal blockade. They do have an advantage in manpower, not overwhelming, but fairly commanding. Despite their resource handicaps their control over industry and population makes them strong, they have a good shot at victory. The Feds have an initial material advantage and will possess most of the tanks and planes, as well as having a major naval advantage over the CSA and AUS which should allow them to blockade effectively. They will also have a practical monopoly on American oil and a strong natural resources advantage in general. Federal manpower is a close-ish second to the CSA. The Feds also have the strongest potential for foreign support, with the probability of Entente aid and ports and a land border over which they can receive foreign aid and trade. The Feds are also the only ones who can expect credible outside intervention, with the possibility of realigning the PSA and New England, and the small chance of direct Canadian intervention against the CSA. The Feds also have a lot more land, and, unlike their opponents (especially the CSA) can trade land for time safely. MacArthur's charisma and hamminess will also be an asset. I'd say the Feds are the favorite for victory and practically can't lose if the pacific states stay with/rejoin the union. All in all, the Feds are most likely to win, the CSA second, and the AUS least (though still a possibility if the Feds and Reds chew themselves up first).
EDIT: Btw, my analysis is based on the Darkest Hour version of the mod, so it may have events that the HoI:II version does not, as well as other differences (such as NYC being red, the possibility of a Curtis admin, Canada seizing New England and Alaska, and the possibility of Hawaiian independence).