Being this is the first time you will be playing these powers you should take a look at YoungGrasshoppers strategy videos. He has done an outstanding job on laying out what each power should do. Once you click on the U-tube links, there are many more to scroll down on the right.
Russian video link
USA video link
France–Best thing you can do with the French is roll really really good against the Germans as they take your capital on the first turn LOL. Seriously though if you end up killing German art and some mech or heavens forbid a tank you have done a great job. Much will depend on the Germans, and if they are greedy and try to take all three French territories making them more risky battles. Other then that start moving your W African and Syrian inf towards Egypt starting on your first turn (don’t forget). Your N African territories can be taken pretty easily by Italy if they want them, but most axis players avoid them knowing that the US will just end up with them and be able to collect the income (as French the allies can’t collect income from them). If the Italians don’t take them out those French inf can reinforce Morocco or follow the US across N Africa. Who knows once the US makes a landing in Europe a couple of those French inf can hop onto a US/UK transport and make it to their homeland. Most times your mini French navy (sz93) is sunk before your first turn, but if not try to get them to safety, if alive they can reinforce the Western allied navies. Move your dd off Madagascar towards Egypt, again to reinforce your Allied navy positions.
Russians–First thing to point out is to pull back all your inf off the front on the first turn, and to temporally fortify Leningrad from an easy Amphib (you will most likely evacuate this VC later though). You won’t be able to hold back the Germans when they come so don’t give them easy kills. When they attack, most Germans will supper stack in E Poland and go south of the Marsh targeting your Ukrainian IC as they move towards Moscow (leading to the oil NO’s to the south). Like I said you need to fortify Leningrad early against an Amphib, but don’t make the mistake of trying to defend it too long (slow moving or dead inf can’t defend your capital). You need to look at moving your Leningrad inf the turn that the Germans attack or the German stack will beat your Leningrad inf to Moscow unless you can delay them (need UK fighters in Moscow).
As the others pointed out building inf is key in the long run. The 9 inf 1 ftr is a good purchase in general, however I also like to build some art in the forward bases (Leningrad and Ukraine), so my first purchase might be 5 inf, 3 art and a ftr (might even mix in a mech occasionally for Leningrad because mech can move back to Moscow double time). The Russians need to do a defensive withdraw from both these ICs, meaning as you evacuate, you set-up a counter attack so you have the option to re-take (trade the territory) so the Germans are delayed from building in your former IC.
Depending on what your German counterpart brings to the front, with a few art you might be able to strafe his stack of units as he closes in on Moscow. I only pointed this out because it sounds like your group might be fairly new to G40. If the Germans pull into Bryansk and don’t have the numbers, forgot to bring AAA guns with them or w/o German planes you might be able to strafe them with everything you got (hit and run). This is a risky move, but could lead to high reward.
Another tactic the Russians can pull off is to take Iraq. Besides getting the 2 IPCs for the territory, it is a pro axis neutral so you also get the 3 IPC bonus (worth 5 IPCs overall each turn). Get an inf, your mech, tank and air ready to strike (from Caucasus) the turn that Germany attacks you (you are no longer a neutral Power and can invade the Mid East). You need to take NW Persia first, then on to Iraq. The UK may be able to take NW Persia for you which will allow you to blitz into Iraq with your mech/tank and air. Your surviving mech, tank and air should be able to get back before the Germans threaten Moscow. This move allows you to keep your income up as the Germans take your land.
Finally you need to have good communication with your allies (especially UK). A good German player going straight Barbarossa will have Moscow ripe for the taking around turn 6 if you don’t get help. Plan on getting some UK fighters to Moscow. You need to plan ahead because unless the UK builds an IC in Persia, it takes 2-3 turns to get UK fighters to Moscow. One route is move planes to Scotland (be sure to move some inf and AAA for protection too). From Scotland (airbase) you can land on Russian safe/fortified territories in the north (Archangel or Nenetsia) then to Moscow next turn. From Egypt you can also fly to Middle East or southern Russian territories that are safe, then on to Moscow next turn. This sounds crazy, but I have also flown in UK/US bombers to Moscow just to tip the scales of the attack, or cause a delay. UK/US bombers can make it from Scotland directly to Moscow in one turn. Also have the allies keep sz125 free of German warships so you can get that NO, until the UK starts landing in Russian territories.
The USA-- A force to be reckoned with once at war, but as the others have said USA must be decisive. Pick a theater dominate it, and play defense on the other side of the map. At some point you’ll have to switch gears, but avoid going back-n-forth every turn. Spend most income for 2-3 turns on one side, then to the other side for a couple turns etc… Much of what the US does is reactive to Japan because they decide when the USA can come into the war. If the Japanese don’t attack J1 (J2), I’ll probable spend most income in the Pac for the first few turns to get on even par with Japan. So capital ships it is on US1 because you can only build 3 ships in the Pac until at war (followed by many dd’s). Plus the US can move more freely in the Pac theater by rule.
Your little buddy Anz is key in the Pac, they can build navy and combine to help defend your US fleet. Queensland offers air cover and is a great staging point for the US. In the Pac the US is the hammer (destroyer of Japanese ships), and Anz is the clean-up crew finishing off Japanese capital ships that are damaged and grabbing money islands, so build accordingly. I will also occasionally split my US fleet and sacrifice some as long as I have a good counter attack including Anz (of course Japan has to take the bait). Like some else said you’re looking for mutual annihilation because the US is able to replace losses, but Japan really doesn’t want to buy ships (need land units in Asia). I’ll also have a couple US loaded transports ready if I can break though. Look for openings when the Japanese air force is tied up (like when they are attacking India, or China)
Europe is a bit different, you still need a navy, but loaded transports are key (and lots of them). You need a strong enough combined allied navy to be able to take a hit from the axis and survive that could include a double attack from both Italy and Germany (keep watch). Once at war the US normally stations at Gibraltar because it offers several options for landings in Europe (good place for a UK air base for added air cover too). UK can also be building ships in Canada at the same time and join you at Gibraltar. At some point you will have to make a landing in Europe. Use the turn order and have the US take land (to grab or build an IC), and have UK reinforce with all available land and air units so you can hold territory (should also include some AAA guns). Some times this might include a stop to London to pick up more units (possibly delaying your attack). If you are going to Norway you may have to deal with the German navy. If in the Baltic the German navy can counter/resupply Norway. It can also be used to suicide your fleet with an air strike after you make your landing in Norway (or Normandy).