As for timing:
In the Fallout universe, October 23, 2077 is when The Great War started and ended.On that day, all nuclear capable countries (USA, China, and USSR mainly) fired nuclear weapons at eachother, then the world fell into nuclear holocaust. People in the USA (not sure about other countries) survived by sealing themselves in nuclear protected Vaults. Others used Nuclear Preservation Shelters found on some street corners in large cities.
Two hundred years later, in 2277, the events of Fallout 3 take place. In 2281, the events of Fallout: New Vegas take place. I set my story between these because I liked the events of Fallout 3 (And New Vegas), and plan to make some references eventually.
Oh, it's based on that
Fallout! Ah, that makes sense now.
EDIT: What about countries who weren't nuclear capable? Did the superpowers bomb them, too?