WD40 is what I normally use. But I wouldn't use it on plastics. And I normally spray it on a towel, paper or cloth and then use that towel to do the wipe / scrub of the gunk. Goo Gone is probably the safer bet. Nail Polish with acetone. Gasoline as long as you don't mind the smell and let them vent a while before sparking things up. To be used semi-polish like, not full dunking. Pluses and Minuses for each. Smell, flammable, abrasive, residue, yada yada yada...
Do you just want it to stop being sticky? Or something else like fresh taped on velcro. The residue of some of these will keep future sticky from adhering to the surface. At least not until it's been clean up. If you just want the sticky to stop being sticky some baby powder or something to cake that part could help. Works for patches on bicycle tubes. But for a device that generates heat, you pretty much have to remove the sticky, as the heat makes it sticky again. I have a headphone preamp like that, racked via double sided tape by the previous owner. PITB, I could probably clean that up, but for a $20 device, hardly worth the effort IMO. For now I just put one of those wash rags under it, 18 pack for a couple bucks at WalMart. Keeps it from scratching whatever it's on to.