I can think of three options, none are perfect, but each could be tinkered with to get what you want:
In the Light of a Ghost Star – This is much further in the future than you intend. But it has incredibly simple rules which are easy to customize. Also I made a psionics supplement for it here. I had pretty good success running it.
Mutants & Machine-guns - A loose, fairly tongue-in-cheek system. Free.
Mutant Future - Basically a cleaned up clone of early edition Gamma World. Less light than other games mentioned.