Use prewar money just like caps, trade with it. You can carry as much as you want it does not have any weight. I could find no other purpose for it. Storywise it just makes more sense to find prewar money in a prewar building than a bunch of caps.
You can also use it as ammo for the Rock It Launcher. The fact that it has no weight makes it handy for this particular use, but as stated above it can be sold for a fair amount of caps so you might be better served using it in a trading capacity.