I'm not a professional historian or anything, but I can give my opinion on this.
The Italian army in WW2 had two major problems - not only was their industrial base sorely lacking in comparison to their neighbors, they also suffered greatly from endemic corruption and inefficiencies caused by fascism(Germany suffered these too, but had inherited much stronger institutions as well as a tradition of perfectionism that kept their industry from cutting corners - for better or worse). In both the army and the navy, competence seemed to inversely correlate with rank, so I'm not sure their officers should have anything but a pistol. Their elite forces, on the other hand, were the bersaglieri(singular bersagliere), identified by the black feather stuck to their helmets. They had minimum height requirements as well as very high standards in both physical performance and marksmanship. Giving them the MP40 fits since historically Italy needed a lot of aid from Germany, and you might want to consider giving them a second power and not giving the officer anything.
As for the other armies, giving the US marines shotguns is fine and adds a bit of diversity to things, though flamethrowers would also be very fitting. The British commandos, at least in WW2, were picked for intelligence and initiative and were a rowdy but highly motivated bunch, and of course they underwent much harsher training than the general infantry. Of the two weapons suggested, I'd say the knife fits them better, though it'd be a bit odd for them to have only a knife attack and no gun. Oh, and did you confuse the Browning and the Bren machine guns? Because the British Bren LMG would fit them a lot better than the American Browning HMG.
I have no particular comments on the Russians, though I'd like to note that a lot of Western historiography of the eastern front is based entirely on German sources, who were obviously quite interested in covering their own asses. The red army was never known for its tactical ingenuity, its approach to equipment was always 'what corners can we cut to produce more faster?' and both its soldiers and factory workers were illiterate peasants but after the initial shock of Barbarossa wore off it showed itself to be very effective on the operational and strategic level, best evidenced by the late-war Operation Bagration and the Manchurian Operation. Raw manpower alone does not win battles - force concentration does.
I think making the German elite be a stormtrooper is a good idea. The SS have a lot of baggage and were selected on a basis of political reliability, so while they had high morale and the best equipment, the actual quality of SS troops varied wildly. Also, while the equipment you picked is good, you might want to consider giving the soldier the MP40 and the stormtrooper a flamethrower(and a gas mask), especially if the US marines keep their shotguns. Gas mask, flamethrower and an all-black uniform just screams WW2 German to me. Finally, I'd like to note that if I was going for realism I wouldn't give their officers a fear effect, but it fits the superhero comic aesthetic of this game just fine.
Finally, giving the Japanese ninjas is very silly, but again it's not out of place in a superhero comic. Japanese officers did have katanas but they were cheap mass-produced status symbols rather than actual weapons. I'd say have them use their pistols. Also, the Arisaka is very fitting for the infantry, but it's too bad there's no bayonet attack. Only army bayonet-crazy enough to put a bayonet mount on their machine gun. Also, if you want a more realistic special unit there's the Special Naval Landing Forces(Rikusentai).
Hope that helps.
