I would use an old toothbrush first; that stuff might come off easily with just alcohol.
Are you talking about the leaves (stator/rotor plates) - or the chassis of the variable cap? If you are referring to the plates - check with a magnet to see if they are aluminum - if so, what you see is likely corrosion (aluminum oxide) which can short out the cap and definitely cause noise and other problems. If you can get the cap out, you might try spraying it a few times with a solution of "Aluminum Jelly" (available at the hardware store) and rinsing it with warm water between treatments. I'd be EXTREMELY careful with any brush since those plates bend easily and it can be next to impossible to fix once bent.
Ultrasound is definitely the way to go if you can get the tuning cap out without destroying the set and if you have around $150 to blow for a machine.... A doctor friend of mine used one to clean his instruments prior to sterilization - he used a pinch of baking soda in the water to facilitate the cleaning action - much cheaper than the stuff they sell at Harbor Freight....