I'm not convinced any of these countries could be taken over wholesale, no matter who the adversary.
I would agree, occupation of any of these would be incredibly costly if possible. Occupation of 3rd world shitholes is a monumental feat, good luck with these ones.
A conflict among these sides would have to end with a negotiated peace, total destruction of one sides ability to wage war, or a 'tie' (plant destroyed).
Historic 'conquering' wouldn't be possible.
Another factor not really considered is allies
I think that was intentionally left out because it complicates things in an unpredictable way.
Allies would be a factor though.
I'm not convinced any of these countries could be taken over wholesale, no matter who the adversary. All countries involved are incredibly big. Russia's advantage is the vast swaths of land to fall back into and geography. USA's advantage is the road and rail systems, distributed population centers, and geographical distance from Asia and Europe. China's advantage is the sheer number of people they can throw at the problem, and geography is also on their side.
Like @InnocentBystander said, after 6 months or so it becomes a battle of who can manufacture supplies the quickest. The USA was great for this for WW2, Russia lagged behind for a while and it showed--they just always had more bodies to throw at it, weapons or not. Nowadays China handles most of the manufacturing in the world, no doubt they'd be able to take advantage of that at a moment's notice. Quality might be a concern, but quantity wouldn't.
Another factor not really considered is allies. The US would have the backing of countries like the UK, Canada, and Australia as well as a large portion of western Europe. China and Russia would probably have the support of the middle east at this point, given poor historical relations with the USA, not the least of which being Iran. There's certainly some wildcards here like India and Pakistan.
I feel like this would end up in a stalemate. If it goes nuclear then the game is over for everybody, and I wouldn't put it past Russia to have a scorched earth policy--literally in this case.