Fallout (the original) is not really the start of the story so to speak. Rather it's a prequel to a game called "Wasteland" which itself had a spinoff of sorts called "Fountain Of Dreams" some like to deny it but the links are obvious. One minor link is the "Firelance" weapon and the aliens in Fallout 3 being a sort of inside joke to people who played "Wasteland". Back when "Wasteland" came out technology was limited and a lot of the story elements came from a book of paragraphs that was packed with the game. Instead of in game text dialogue you'd be told to say "read paragraph X". Well one of the things they did was include false paragraphs for people who read ahead for spoilers. One recurring thing that "zapped" some people was the mention of Aliens with their firelances in more than one place. Anyone who read the paragraph book (while playing the game for spoilers, or otherwise out of curiousity) would get this.
At any rate, the way things play out in simple terms is that in Fallout 1 you rescue a girl named "Tandi" who later goes on to found the NCR and a group called "The Wasteland Rangers" in Fallout 2. These Rangers are the protaganists of Wasteland (your party). While Bethesda might deny it, some of the design desicians made with Fallout 3 make sense in regards to the overall history. Like for example WHY the game was relocated to Washington DC. The answer is more or less that other events are taking place on the left coast and key locations like Vegas.
It's also notable that during this time period the major stronghold of the West Coast Brotherhood Of Steel (the Guardians in their Guardian citadel) will be attacked as a result of it's seperationist policies and overrun by the Wasteland Rangers. This is quite probably why there has been no real contact with or attempts to reconcile by the DC Brotherhood and it's Outcasts.
Now granted, this is not perfect due tot he amount of time that passed between games, but that seems to be the gist of events. It's surprising how much sense a lot of things make if you consider Wasteland in the mix.
At any rate in Wasteland there are 5 "races" you can choose from. US, Indian, Mexican, Russian, and Chinese. This leads me to believe along with a few other little hints that the US was indeed facing a combined USSR/Chinese force, and that quite probably Mexico tried to invade at some point as well. "Tribals" having been around that far back (a quest involving getting into Junktown by rescueing a kid named Red Hawk is crucial)
Current events have changed from what they were back then, and this is why I suspect too many specifics have been avoided. Of course that could also be because of the upcoming Anchorage download which could add a lot of details and might prove or disprove my supposition.
The way things seem to me is that the US continued to be a group of idiots and refused to take action against China's patent violations, resulting economic growth, and use of that economic growth to build a military, combined with Russia's regression to it's old ways (Ukraine Asssination attempt, combined with recent events there and in Georgia). The US probably awaiting an ideal solution while sending out diplomats when it should have been taking military action long before it actually decided to do anything.
Lax internal security due to the constant battles over civil rights also leading to the US being heavily infiltrated by Chinese intelligence forces and special operations troops. They come in as immigrants, and next thing you know they are effectively running things like Mama Dolce's.
As a result a bit of what President Eden (no spoilers from me there) says on the Radio about incompetance is actually true.
When things came to a head I'd imagine the US didn't want to get involved, and sent diplomats. Europe became divided between sell outs (socialism is arguably the extension of communism) and those holding onto more democratic/capitolist idealogies. Not feeling that we had the guts to actually launch WMD the Chinese and Russians landed/took action, and nations like Canada sided with the European sell outs and got involved too. Finally the US responded but unlike World War II were not able to save things that far gone
in the 11th hour. Powered Armor troops maintaining control, decimating Canada, retaking Alaska, and pushing out their troops. Eventually it came down to a nuclear exchange, and yes, America did push the button as well. Though who fired first is probably a matter of debate.
This is my guess from a lot of things that were said. Europe being so divided even under a EU (or Commonwealth in this case) probably fratricided. I'd guess given how the radiation is clearing in DC and such that the US actually "won" the nuclear exchange which is why so much is relatively intact and you see the beginnings of recovery. Things like missle interception systems on submarines (between us and them), and the possibile existance of a secret "Star Wars" system (maybe not so secret in this alternative timeline, what treaties may or may not have been established with the Russians is debatable). This would be why DC isn't a kilometer deep crater despite being the #1 priority target for anyone wanting to take out the US.
Given that the US has enough firepower to destroy the world ten times over all by itself (more nukes and WMD than anyone else)
I would imagine there isn't going to be much left of the rest of the world. What's left in Europe more or less depends on what happened with say French Socialists, The UK, and of course US missle bases in places like Germany. But I'd imagine Europe might literally be a crater (as much as Europeans might not like that idea, wanting their own chance to be cool and post apocolyptic as well).
I'd say Australia and perhaps parts of Africa (Farmham's Freehold anyone?) would be the most likely to have survived in any nuclearly minimal fashion. Russia and China might have some intact portions but probably only the parts that were the most horrendously rugged and inhabitable. Most of China's livable land, major cities, etc... wouldn't even be ruins. In Russia you might see
some isolated groups of Russian survivors living like Eskimos in Siberia or whatever.
Such are my thoughts.