How can you get the old smell out of drawers?

Some people save those little dry packets that come in over the counter vitamins and minerals or medications for their drawers. Also, sometimes when you buy items they will include larger dry packets in them. Save them for such a need as a damp drawer too.

How to Eliminate Odors in Wood

Your best hope for sealing in any odors is shellac. It makes an excellent barrier coat over all wood species, and it sticks to almost anything. Zinsser makes a great product for this purpose, called Bullseye SealCoat. It’s a clear dewaxed shellac that you can apply to those drawer interiors easily with a brush. It dries quickly and should help to diminish mice, mildew, musty, smoke, urine smell. And since it doesn’t contain wax, you can apply other finishes like lacquer or varnish over it — they’ll stick just fine. SealCoat is also handy to have around the shop as a general purpose wood finish and sanding sealer. So, I’m sure you’ll find other uses for what’s left of the quart you buy.

You could put cedar blocks in the draw you could line the draws or you could take out side scrub well and let dry after hosing down or spray paint the inside to seal them

Newspaper and/or charcoal (not brickets). You may have to replace them a few times to get rid of smell totally. I used this in a freezer that had been stored with lid closed.

Coffee grounds is the best method to take out any smells. You can scatter them on the bottom of the drawer or put some into a shallow container. The grounds should last for several weeks and be replaced as needed. Just buy a cheap brand to be used exclusively for this purpose.