How can I clean my cedar lined dresser drawers?

I have a dresser that my parents purchased in 1954. The drawers are cedar lined and it's in excellent shape...I've used this dresser for 15 years now. I moved from California to Upstate NY during the summer of 2005 and the mover put my things in storage for me (because my family and I traveled for 4 months before landing in NY). The mover didn't cover any of my belongings with sheets or otherwise and my stuff was in storage for 9 months before I bought a house. Now my dresser drawers don't keep anything fresh. I wiped them down with a wet cloth and even sprayed them with essance of cedar, but after a month my clothes end up smelling very stale and old (like sheets that have sat in an old closet for way too long). This was never an issue before, so I'm uming the drawers must have absorbed dust and what-not. My clothes (esp my sweaters) used to smell fresh...with a light hint of cedar...before my dresser was in storage. Please help!