Forgive me if this is a joke that I'm not getting, but they wouldn't be useless at all:
1) Bitcoin is a p2p distributed network with nodes all over the world. Even if a nuclear attack took out the entire US, the network would continue to work as long as segments of the Internet did (and recall that the Internet was originally designed to protect US data networks from nuclear attack).
2) It's quite simple to spend Bitcoins as long as you have access to a Bitcoin node (see above) and a copy of the 32-byte private key string corresponding to the public Bitcoin address the coins were sent to. This short string of characters can be written on paper, etched into stone, whatever.
The receiver can't be sure that the Bitcoin hasn't been double-spent without waiting on changes in the block chain to propogate; that's not easy in the middle of a nuclear wasteland.
