Remove all objects from the wood. If the mothball scent is in your dresser or wardrobe, remove the clothes and any other items and set them aside. If the wood item is a dresser, remove all of the drawers.
Create a cleaning solution using equal parts of isopropyl alcohol and white, distilled vinegar.
Dip a sponge or clean cloth in the solution and wipe down all of the surfaces of the wood furniture. Allow the wood to dry and air out in a warm, well-ventilated area or outside.
Smell the wood after it has dried. If the mothball odor persists, repeat the process until it disappears completely or is, at least, much weaker than it was before.
Fill small bowls with either cedar chips, activated charcoal or baking soda and place them inside the wood furniture. Place one bowl in every compartment or drawer.