My daughter stored her prom dresses in my basement for several years. It's picked up an odor akin to cigarette smoke. She took it to a professional dry cleaners. They said nothing could be done. She now has them hanging in her garage.
I have removed terrible musty and mildew odors from clothing by putting a paper envelope with fresh coffee grounds (right from the can) in a plastic bag with the garments. I folded the garments and put the envelope with coffee in the middle. It may take a week or more but leave it until it is odor free.
I put a bag of charcoal and the fresh coffee grounds into my huge plastic city issued trash can and closed the lid and two days later the horrific odor was gone. Try it with the dresses in a plastic bin or large trash bags. Good luck!
Prom and dancing can lead to sweating and, unfortunately, prom dresses are often difficult to clean. This is a page about how to remove underarm odors on a prom dress.