In the spring of this year, I rented an older house that had smelly wood kitchen cabinets. The house had been vacant and closed up for a month, so I aired it out a few days but no change. Friends and family had a variety of suggestions I tried. I sprayed bleach and soaked and wiped: no change. I put cups of baking soda in the cabinets and even rubbed it into the wood: no change. After a month, no change.
I remember someone a few years back telling me they had used charcoal for their basement mildew smell. So I got a bag at Walgreen's, put three briquets in each of 15 old plastic yogurt cups, then placed them in all the drawers and cabinets. Voila! One cabinet smelled no more in half an hour! The rest took a few weeks and the cabinet under the sink took approximately one month. After 4 months, I removed the charcoal and the smell returned in the drawers. I put one briquet back in each of those areas and the odor is gone again.
Be sure to get a charcoal that would require you to add lighter fluid if you wanted to burn it. You do not want self-starting briquets that are coated with lighter fluid. Besides being dangerous in your home, they're coated and don't work well as an odor eater.
I found two minor drawbacks. One, if the containers tip over, the charcoal leaves black residue on the shelf or whatever it falls on. But it is easily wiped up. Second, when I had three briquets in every cabinet, I could smell the charcoal. Now that the moldy odor is gone, I just have a couple briquets in a few places and rarely smell any charcoal.
Overall, I was amazed and rate this as a top household solution to cabinet mold and mildew odors.