Thank you for accepting my suggestions as your official answer. I've
reposted the material below, with some extras.
Musty odors in closets are almost always caused by mold or other
fungal growth. Even if the closet does not seem damp, if it has no
ventilation source and is kept closed off so that the air does not
move, there can be a mold problem.
I used to have a musty closet. The problem was solved with the use of
a closet dehumidifier that contained silica gel. In about two weeks'
time, the clothes and sheets in the closet no longer had that faint
musty, earthy odor.
Here's an article on dehumidifying closets:
i-dehumidifiers.com: Closet Dehumidifiers
Some closet dehumidifying products that are for sale online:
Froogie: closet dehumidifier
A friend of mine had musty-smelling sheets and towels, and she solved
the problem by using the Gonzo Odor Eliminator in her closet:
"The Gonzo Odor Eliminators are volcanic crystals that will rid your
home, car or basement of unpleasant odors... The Gonzo Odor
Eliminators are all natural, odorless, non-toxic volcanic crystals
with millions of surfaces and channels containing a negative charge.
The Odor Eliminators act like a magnet does with metal; they attract
and hold all odors to keep the air clean and smelling fresh. This is a
great item to keep in your kitchen, basement, closet, car, or any
other area where odors may linger."
The Gonzo Corp: Odor Eliminators
This is the product that worked for me:
"DampRidŽ Odor & Moisture Absorber eliminates musty odors caused by
stagnant air and creates fresher, healthier air. Designed to absorb
excess moisture in areas where electrical dehumidifiers are
inconvenient, this freshener non-toxic, septic safe, non-electric,
scented and environment friendly. Each 14 ounce box consists of 1
large hanging packet of white pellets designed to maintain the
humidity to a safe level. Each box will last approximately 60 days.
The freshener beads turn yellow when it is time to replace the packet.
Convenient hanger type hook on the pack ensures that it does not
occupy extra space and almost blends with your clothes line. Protect
your favorite plants, clothes from damage due to moisture. Use it in
closets, cabinets, bedrooms, bathrooms, laundry rooms, basements etc."
Amazon: Damp-Rid Closet Freshener
I have had no experience with electric devices for deodorizing
purposes, but there are several ionic air purifiers on the market
which are designed for use in closets. Here are two such products:
"NexxTech Ionic Closet Freshener...
Freshens your closet: Ionic technology pulls pollen, bacteria and
odor-causing materials from the air, leaving your wardrobe smelling
fresh and clean. Two power settings give you the freshening power you
need. Add aromatic oils (sold separately) to circulate an even more
Easy to place: Mount the freshener on the wall or simply hang it
Smart design: This smart device runs only intermittently to save
power, using six C batteries or a 9volt DC adapter (both sold
Circuit City: NexxTech Ionic Closet Freshener
"Banish musty closet odors and keep your clothing fresh and
clean-smelling with the WindChaser IMC-1 ionic closet air purifier.
This compact unit easily stands on closet floors or shelves without
cluttering your space, but it can also be mounted on walls in your
closet or laundry room. Its advanced ionization technology eliminates
airborne particles, mold, and musty or smoky odors, keeping your
fabrics laundry-fresh! With no messy filters to clean or replace, the
IMC-1 requires almost no maintenance. Simply clean off the metal
collection plate, and reuse it."
Air & Water, Inc.: WindChaser Ionic Closet Air Purifier IMC-1
My Google search strategy:
Google Web Search: closet odors
Google Web Search: closet desiccant
I hope this is helpful! If anything is unclear or incomplete, or if a
link doesn't function, please request clarification; I'll be glad to
offer further assistance before you rate my answer.