Europe was in bad shape before the War happened, i assume Africa, South America, most of Asia were still 3rd world countries before the War, and China obviously got nuked like crazy. Also the War between the US and China was around resources, i can only guess that if the two greatest powers were fighting over resources, they were sorta cutting the rest of the world off. So the rest of the world was in bad shape pre-war, however they probably weren't hit as directly, but i don't think they would have vaults.
In conclusion, everyone got boned.
http://fallout.wikia.com/wiki/Resource_Wars
http://fallout.wikia.com/wiki/Europe
http://fallout.wikia.com/wiki/China
http://fallout.wikia.com/wiki/Middle_East
http://fallout.wikia.com/wiki/Soviet_Union