According to Fallout lore everything by 2077 was powered by nuclear technology. Everything from cars to power grids are all fueled by nuclear power. This would require tiny nuclear reactors, particularly for cars.

Modern nuclear reactors (in our universe) are massive, typically the size of a large residential building. They need all that space for the reactor, the cooling towers and the steam turbines. They are also put well away from cities and towns becuase of the dangers of nuclear radiation, meltdowns and the general unease of the populace for having a nuclear reactor in their back yards.

However there is a different kind of nuclear reactor. Instead of using Plutonium or Uranium, these power plants use Thorium, a more effcient fuel that does not require the massive cooling towers and can utilize a significantly smaller reactor. Rather than using steam, Thorium reactors uses a C0₂ system that is self contained. Essentially these are already small enough to be placed in say... an underground bunker. In time technology could eventualy make it plausible to put them in cars.

Here's the link

http://world-nuclear.org/info/inf62.html