I’ve been off on medical leave for a while and so my dress shirts have been in the closet for over a month. I put one on the other day and found it smelled musty/dusty. Usually they don’t have enough time to pick up that smell. I wash them and where them in a week or two.
Any suggestions for getting rid of the smell. I took a bar of soap and put it in an old sock and hung it among my shirts. That may help.
Lavender or cedar may help. If the closet has an incandescent light bulb in it, try leaving that light on for a few days, with the doors open. That’ll help dry things up, if the smell is a result of damp.
Generally, I leave closet doors open for ventilation.
If you can tolerate it, get some scented fabric softener sheets and strew them around. You can tuck them into the corners and even under baseboards and molding a fraction of an inch.
Generally I leave them open 'cause I’m lazy… 
Get a bottle of Febreze and spray the clothes and the closet. It will freshen up your closet.
Generally I leave them open becuase all my clothes are on the foor in the way of the door.