With the high humidity we have had lately I would try putting a box of baking soda in each drawer and closing it for a few days. It should absorb the odors! I know my wood (oak) dresser had a funky smell for awhile.... I did this and also kept the air conditioning low so no added humidity could get in there. Either that helped or I got used to it :) I also always place fabric softner sheets in all my drawers to keep them smelling fresh and to keep the clothes from picking up any of that weird scent.
Here is a link to help you get rid of all kinds of different odors in things, including wood!
Good luck finding what the cause is! If this does not work or another idea from people then I would return it. Make sure you know how long you have so you do not go over by one day before you call! (I have done that too often lol)
Many blessings to you and the new baby on their way!