If going Russia first, I suggest a bee line straight for Moscow, the physical act of taking either of the other victory cities in Russia puts your stack 2-3 turns behind. I would start this attack no later than round 2.
If you secure Moscow first, the other two will fall within 2 turns, as Volgograd (Stalingrad) is two turns away from Moscow, or hit it the turn after Moscow with your reinforcements that would have built up your stack. If you are lucky the Russian will make the mistake of trying to hold either city and garrison troops there that won’t be in or make it to Moscow in time as you by-pass them.
Novgorad (Leningrad) is easy to reach by sea mid-game or with your reinforcements that would have moved toward your stack, the turn Moscow falls.
Ideally, the other 2 cities will be vacated as Russia retreats to Moscow to force a big battle there. If not, try to capture all three the same turn if you have Egypt and are trying to end the game by cities. Otherwise, use your Moscow leftovers to grab Volgograd and focus on defensive builds that hold the 8 cities. Grab Novgorad with units that were marching into Russia or by sea if possible.
Italy’s job will be to secure Egypt. Once they have it, it may prove possible to assign Volgograd as their next objective as they have two routes to get there. They may be busy just holding their capital, but that depends on the allied player(s). This would help Germany to keep their offensive inventory concentrated and more devastating vs Moscow.
Unless UK1 builds transports for S. Africa it seems easy to seize Egypt even with a UK1 factory by turn I2 and without an Italian fleet as long as you had 1 transport that could send two units to Alexandria I1.
Remember Italy can trade its capital if it means forcing the allies to commit transports (as they are now out of position) and Germany is in a position to liberate before it is upgraded to a Major Factory (two turns before it produces), this may seem silly, but if it permits you to have more Italian units in the field at Stalingrad or Egypt it may be worth it. If Rome becomes your 8th city for the win, that is much closer to Germany than Moscow.
Some suggest sea lion is the way to go, but I think it gives Moscow too much time to build up and stall longer while the U.S. tries to win it.
Keep trying, it may prove hard for the axis to win in Europe only. Global may be the preferred game.