How many people can live in one Vault?

I would reckon in an average sized vault roughly 80 would live there, though I bet there were giant ones in which a few hundred could live.

It varied depending on the size and purpose of the vault.

Some on the West coast could hold a thousand or so people. Vault 112 could apparently fit 80, the others could fit around a few hundred or so. Difficult to give a specific number as we never see a complete layout of a vault.

I'm writing a play. It's a cross between Glee and The Road.

Vault 68 and 69 had 1000 people each.

Even though the Vaults all had a different purpose, their design was basically the same. They were intended to house 1000 people apiece (122 Vaults total) and only needed 500 beds as they were implementing the military practice of "hot racking."