Lay a large plastic bag on the floor. Tip the whole contents of the drawer onto the plastic bag. Clean out the drawer and only put back what you really want.
Then, if you can, throw everything left on the plastic bag in the garbage bin.
Drastic, I know, but fast. And you'll feel very good about it very soon.
I know we want to recycle and see that every pencil has a good home, but occasionally it's easier not to. With your newly refurbished nearly empty drawer you'll be more productive and you can resolve to recycle everything from now on.