Since I asked what works for everyone else(and we've had great responses so
far), over the 30 plus years I've worked on cars,  here's some of the stuff
I've tried.

Kerrodex- tube of pre treatment for your hands ie rub it in before working
in the nasty.  More designed for fiberglass resin, but any barrier you can
wedge in under the cuticles before the grease gets there, must be a help.
Orange Pumice cleaners-  Excellent but not the ultimate.
Goop- Way too much petrol in it.  Need to chase it with the orange stuff to
hide the smell.
Nail brushes- Wife found a green handled nail brush somewhere that had the
stiff bristles for the fingers and a single row of stiff bristles hidden in
the concavity of the handle to scrub out the grunge under the nails.  Very
effective tool.
Gloves- A no brainer, but the nitrile gloves can be a little difficult to
find on short notice.

When I have to be Sunday morning church-immaculate, I will jump in the
shower after getting as much grease off as possible with the orange
pumice.  After a hot soaking shower has hyper hydrated the skin, I take a
plain old bar of soap and jam it up under all 10 fingernails and then
continue the shower.  After all that soap has sat underneath the nail beds,
the aforementioned brush will scrub most of the grunge out and then a
finger nail cleaner will usually get the rest.  A very long and laborious
process making me wish I'd shopped for the gloves before I disabled the
Vanagon.

DM&FS