The original(blue) Dawn works for organic greases, medium well for petroleum-based crud. The orange-based hand cleaners work pretty well for most automotive crud, with or without pumice, if I need really clean hands, I'll do some hand laundry using clothes detergent and some red shop rags. Nothing removes MoS2 from hands except time, ditto graphite. I'm not a big fan of gloves for mechanical work, can't keep hold of wrenches or parts and my hands inside become very slippery with sweat. Same with any type of coating or hand creams. Nothing like squirting the one and only nut in existence down into the guts and then trying to fish it back out. Only time I really take to gloves is repacking and installing CV joints and I thankfully don't do that more than once a decade. I have used some stuff called Krud Kutter for various cleanup tasks, it works pretty well on hands but contains diluted lye, so will dissolve your skin eventually. Lowes has carried it, have seen it elsewhere, too. They think very well of it, so I haven't bought much of it lately. It's a purple stuff replacement, only it works better. Works well for cleaning off greasy fingerprints from fresh latex paint.
Stan