I keep a bowl of white vinegar on my stove to keep cooking odors down. When a closet or room starts to smell musty or stale, I put a bowl of white vinegar on a shelf for a few days. This usually takes care of just about any smell. It was especially good when my son was a teenager.
(You won't smell the vinegar except when you first pour it.)
Source: Personal experience
I live with my family in a rented house that is very damp, and it smells really strong and musty. Does anyone know how I can get rid of the smell? I live in England, so I wouldn't be able to get any American products if you recommended them. Thanks.