Sunlight and baking soda (dry) can also help remove odors, just be aware of humidity. I'd put out the drawers in the sun with quite a bit of the baking soda for a couple hours and then shake out the baking soda. If you can put the dresser on its back with the drawer openings getting the light/air, I'd do that too.
I have used the charcoal bags with success in one of my car trunks, where the problem was Seattle wet and humidity and a car that smelled like wet dog. In that case, I had to rotate the charcoal bags every few weeks take out the old one, replace with a new one while I dried/recharged the charcoal.
I can report that there was no stainage or anything even with damp as an issue. White charcoal bags stayed white, gray car carpet stayed gray -- smell was much improved!