Well, well, I'd never have thought there were so many variations on washing up at the end of a grubby day. I usually use cold water, although hot does shift the grime quicker as it opens the pores and the sweat then drives out the dirt wedged inside them.
Personally, I use Fairy in whatever flavour Hazel has currently propping up the kitchen house plants. A quick rinse with the first splodge and then the second dose onto a short spined nail brush and a proper scrub all over will see off almost anything. This I follow up with toilet soap (Dove, currently I think) and a dry on the nearest towel. Then - most importantly - a layer of decent hand cream, rubbed well in whilst the hands are still damp. I don't wash up properly for lunch, say, only a quick wash off with Fairy to remove the loose oil etc. Ingrained stuff can wait til later.
However, oil that's been in a sump for a l-o-n-g time will often leave black in the skin and I've found the same as others that sugar or sawdust will help.
I used green Swarfega every day without incident for the better part of forty years. The only reason I don't use it now is that it's one more thing to clutter the worktop and my hands are not exposed to the workshop more than perhaps three days a week.
Acids and caustic solutions may not suit all skin types and although my integument is fairly dense (ask any of my political opponents!) I'd not risk it myself ...
Regards,
Kim