How do I remove musty smell in coat closet?
A dehumidifier should remove the moisture (I've also had success with DampRid) along with some kind of scent remover like Febreeze or something similar, but I'd be more concerned with additional moisture building up. I'd check more into how the moisture is getting in to begin with. The caulk may have sealed the gap but do you know for sure that no more water is getting behind the wall or under the sub floor?

I'd be afraid of additional mold building up or water backing up somewhere and causing you additional damage.