OK, so now hat happens? Stalin was a big part of why The Allies won, but they now have Mussolini...
Well, taking in consideration that Hitler will surely don't want Red Army unit in German soil we can forget direct help in the invasion of French; this in conjunction with the Italian enter at the Allied side mean a Germany occupied in a two front war, a situation that for now she is not equipped.
Basically the need to guard the south will divert enough land and air asset to get a big wrench in the Werchmatch plan.
On the Allied side or better the reformed Stresa Front, Italy for all his military limit mean that the Mediterrean is now an allied lake and there is no African front; the italian air force is more aggressive than the French one and will not really shy from launch bomber mission...sure it will not very effective still the Luftwaffe will need to defend and counterattack and the italian penisula is a good point for launching raid for the RAF.
In land a defensive war in mountain is what the italian army is trained and equipped and at this we need to add the terrain that greatly favor the defender (and make the use of tank very difficult) and the fortification that Benny build there just to be sure...basically the German will face a maginot line that can't be bypassed.
On the Russian side, well the problem is that in 39 the Red Army, thanks to the purge of uncle Joe, a mess with obsolete equipment (the main battle tank is the T-26 that even the anti-tank version of the tankette L3/33 can succesfully engage) and in general need to vast reform (OTL were not completed even at the time of Barbarossa)...add the attack on Baku that even if incapable of destroy or severerly damage the place will surely cause enough damage to slow the place hampering the Red Army operations.
Principals directive of attack for the Russian will be Persia and Balkan with maybe an operation through Afghanist towards India (but is more probable a diversion attack); Finland can be easily convinced by the Allied to aid against Russia a la continuation war.