Place the furniture outside on a warm, sunny day for several hours. This will help air out the odor. If the furniture is too heavy to move, open the windows near the furniture for several hours.
Mist the upholstery lightly with white vinegar and air dry for several hours. Repeat the process until the mothball odor is no longer present.
Wipe the hard surfaces -- such as wood or plastic -- with a cloth damp with white vinegar. Let the vinegar air dry on the surface. Repeat the process until you have removed all traces of the odor.
Fill drawers with crumbled pieces of newspapers. Leave the balls of newspapers in the furniture drawer for 24 hours to absorb odors.