Taking a realistic spin on this sort of back story would be rather difficult. An Electro Magnetic Pulse (EMP) in the upper atmosphere/low orbit would fry a lot of electronics, mess up databases, and cause havoc with the power grid. However, it would not stop firearms from working, and mishandling nuclear materials wouldn't cause mutation. (well, cancer is a kind of mutation, but not a helpful one) Despite the massive numbers sitting in the various national armories, we don't have nearly enough firepower to blow up the moon, nor enough launch capacity to get the weapons there anyway.

Now, if you wanted to shift things to a magical angle, then it gets away from the cliche' of international terrorism and abused nukes. Perhaps the cataclysm has drained most of the magic from the world, making mages far harder to find, and undermining much of the advanced society based on the "technology" of functional magic. Worse yet, the seals on various old evils have weakened or broken entirely due to the new state of affairs - perhaps possessing some faction - leading to the seemingly mindless shock troops you alluded too in the original post.

A rediscovery of the mundane sciences is attempting to cope with the new world, so standard fighters, or chemists that can make medicine and gunpowder are in high demand. Players would of course fit in as the (rather mercenary - but hey, all the factories have stopped so goods are expensive) heroes of the age.

There is a fine line between hobby and obsession. I seem to have lost sight of it some time ago.