You didn't quite answer the rest of my ?'s. The answers would be 'useful'.
BUT, assuming the smell is coming from the 'drawer base', yes, you could clean them w/a mixture of bleach and water. Mix 1 cup w/1 gallon of water and brush them good. Let them dry for like 3 or 4 days since the moisture will need time to evaporate. Then, you can 'seal' the base w/Sand Sealer. This will seal up any openings in the wood and prevent any odors from escaping and any moisture from getting in. You WON'T be able to stain it since the Sand Sealer, well ..., sealed the wood! So, if you're gonna do this, be SURE that the most you're gonna do to the base is poly it. Oh, consider using 'Clear' Sand Sealer. You can read the can in the store as to how it works. (As an aside, when you STAIN a piece of wood, the stain itself has a sealer in it. That's OK because, as you know, you just apply poly after you stain. The Sand Sealer works the same.
You needn't Sand Seal ALL sides of the base. You can do just the inside if you want. You may find that sealing the inside is enough to stop the smell. Do clean ALL sides of the drawer, and all, but for starters only seal the inside part of the drawer to see how the smell is.