Use Q-Tips or a thin, white cotton rag, dipped in distilled white vinegar.
Soak paper towels or cloths in your preferred cleaner (mine is white cleaning vinegar) and place on the tracks. After sitting for a period of time, you can remove the rags and rinse away the nasty.
Old toothbrushes are great for cleaning small spaces!
Slide a rag strip about 3-4" by about 12" under the door that is cut from an old t shirt. Pull it under the door and use something like a screwdriver to gently pull it to the other side. Spray track with a good cleaner and slide the t-shirt rag back and for the under the door track. This should loosen any gunk on the bottom of the door at the same time it is cleaning the track itself. Rinse.
I'd use a small vacuum nozzle and then a tooth brush to get into the nook and crannies!