Considering that the world was supposedly destroyed in a nuclear holocust.
They must have used a version of the neutron bomb, which kills people but leaves buildings intact.
I'm not crying, you fool, I'm laughing!
Hewwo.
From what I understand, it wasn't a nuclear holocaust but just a few weapons were detonated and the radioactive dust cloud circled the earth which killed the population (see/listen to the scene when going to the radio station). It doesn't sound like the US was even attacked or hit with any weapons. It was a UN action so the main fighting could have been Europe/USSR or maybe China.
Conquer your fear, and I promise you, you will conquer death.