What are ammo boxes?

Can you store any of your loot in an ammo box or will it strictly only take ammo?

Ammo boxes contain ammo for various weapons. As for storage, try storing things in a safe place like your hotel room or an abandoned building in a town you frequent.

Is it even possible to store non ammo items in an ammo box?

Why wouldn't it be? Storage is storage, as long as it doesn't respawn, or disappear.

Note the ammo boxes you see inside vendors is NOT the ammo box you see laying about.

Chet tells you about these. They contain bulk ammo (you get a bunch with the one purchase).

Generally the ammo is worse, but cheaper... but this isn't always the case.