It's unlikely that Europe was hit by direct Chinese nuclear strikes as most of the USA's alliances seem to have fallen apart by 2077; after all the USA had already invaded Canada, its closest ally! That would not have stopped Europe being affected by fallout, and as already stated, the Resource Wars had lead to to the collapse of the FO world's equivalent of the European Union with subsequent wars between the European nations.
My feeling would be that since 200 years have passed since the War, Europe is probably a lot further down the road to recovery than the former USA.
The US didn't invade Canada, it Annexed Canada. Symantics Really, but remember, the US Anexed Texas, Oklahoma and pretty mych everything west of the Mississippi River. Canada also volunteered to be annexed (As you find out in FO2) for cheaper resources from the US, who had just tapped into the Pacific Oil Basin the the Poseidon Oil Rig. I imagine if the war didn't end the way it did, they would have beed adopted into statehood. Much like every other annexed state in our country.
Brittan has been with us through thick and thin, so I'm sure they'd be nuked as well. The rest of Europe would probably nuke each other, based off the into of FO1 ("Europe was reduced to quarreling, bickering states"). Last time that happened they almost ended up speaking German. And the US still had China to deal with, so no help from across the Atlantic this time.
So essentially, that leaves the third world nations (South America, Africa, soutern Asia) left. They wouldn't have survived intact for long after the world's end. Between the mini-ice age, depleated Ozone and other enviromental effects (Some caused by the release of the FEV), it would have been chaos. Venezuala probably got nuked, since they could still have some oil, but I doubt they had any left.
Also, one big hint in the war. The US Invented the micofusion cell, so their need for petrolium is nil. Why use gas when you can use a nuke engine? The driving force in the war is petrolium and uranium. The US has an ample supply of uranium, but little petrolium. It could be that while the world wa tearing itself apart, the US was sitting back in an isolationist policy, building its resources (and vaults). When the wells ran dry, we had everything that was left. Hense the Chinese Invasion of Alaska. Also a good staging point to invade the posseidon Oil Rig in the pacific. In FO2, you learn about the price of crude oil, several thousand per barrel. Its in the same note you learn about Canada's PM volunteering to be Annexed to get cheaper oil (The US Administration reponds with how their hockey players will be a great addition to the US).
In the end, I think China pushed the button first. The US Pushed them out of Alaska, and probably started making headway into mainland China (Most likely through Siberia). They panicked, and hit the big red button. We retaliated, and when everyone else saw the nukes fly, they launched as well.
Of all the survivors, I'd imagine Africa, South America, The US (Because of the Vaults and large landmass) and south east asia. No government would survive, and people would probably flock to these location from everywhere else. In a few hundred years, I'd imagine the tables would be turned on the world structure, and the former third world would end up becoming the first and vice versa.