Hi. I'm glad that I saw your post because I have the same problem with a dresser in my daughter's room. It's a dresser from IKEA. Don't know if other people have the same issue with furniture from there. Sometimes I think it contributes to a cough she gets.
Here's a remedy that I read about in the book, Eveyday Cheapstake's Greatest Tips. I've been meaning to remedy the dresser we have.
Place a slice of white bread on a saucer and cover it with white distelled vinegar. Place the saucer inside the drawer or cabinet and close. The smell will absorb in the mixture.
Another idea from the same book is: Dampen a paper towel and set it in a small container. Pour 2 teaspoons of cheap vanilla extract on it. Put the whole thing in the smelly container and close it. Wait for 3 days. Works well, even inside old fridges.
Hope this helps.