Synonyms for Musty (same or very similar meaning)
WordNet sense 1 (covered with or smelling of mold):
moldy, mouldyWordNet sense 2 (showing deterioration from age):
staleWordNet sense 3 (stale and unclean smelling):
fusty, frowstyWordNet sense 4 (having an unpleasant smell):
malodorous, stinky, malodourous, ill-smelling, unpeasant-smellingFrom the ODE community, based on WordNetadd/edit