Soap is a great freshener. Use a hand grater or a potato peeler to cut the soap into smaller pieces. Then put the pieces into a small bowl.
Put the bowl into an area that you notice musty odors. Make sure it isn't somewhere that it will tip over.
A dish of activated charcoal will also help to absorb odors from closed up spaces.
With either the soap or the charcoal, if you would prefer to hang your odor absorber, stuff the toe of an old nylon stocking and tie it off.
Sometimes mustiness is caused by mildew, if you think this is the case (like an antique item) wipe the inside of the drawers with a mild bleach and water solution.
Then, wipe it again with a clean damp cloth. the bleach will kill the mildew spores and in turn freshen the drawer.
That should do it, easy ways to eliminate musty odors from your house. I'm Mrs. Fixit and it's just that simple!