They could run off of virtually any power source you can think of. Nuclear. Solar. Standard 9 volts. Anti-Matter Sublimation. Even Happiness.
Personally, I didn't think much about what it runs off of. Know why? Because everything in the Fallout World seems to not have energy problems. Even a old, rusted computer half buried in trash can still work, assuming it's turned on. Powered Armor, which would require big power sources, doesn't take any energy to run. It has a energy generation built into it, or at the very least a huge battery, and it charges with Kinetic energy.