My usual process is soap and water first, then alcohol, then something like Windex, finishing with something like bleach.
Moving past water-based solvents, and being very careful, I try organic solvents (citrus oil), then naptha (old-fashioned lighter fluid), then acetone.
If none of those dissolve the gunk so that I can wipe it off, I start in with abrasives, beginning with pencil erasers.
I have only found a couple of keys that were actually stained at a penetrating level, where nothing worked to remove the blotch.
Cases are more likely to have really stubborn problems, in my experience.