K.N.
I've found cedar to be effective -- but you need to freshen it up every now & again. Since it's a cedar closet, just take a piece of very fine grit sandpaper & rub it over a few of the planks every few months or so. YOu should notice a stronger cedar smell when you're done. From what I've heard, it's the oils in cedar that repel the moths and, after a while, the wood dries up a bit. Giving it a rub with the sandpaper releases more oils. If you don't have sandpaper, maybe a scrubbing sponge or bit of steel wool would help. Also, it's best if there's a rubber gasket around the door, creating a tighter seal so the blasted bugs can't get in there to begin with. Rotten critters.
Oh -- also I, too, have heard that woolens should be cleaned before storing.
Good luck!