Permatex Fast Orange w/Pumice.
Since I've always got a few cuts on my hands, I tend to wear gloves (the Fast Orange is more for my forearms. I've taken to shaving my forearms fortnightly - grease pilling up the vellus hairs on them tends to hurt when you end up yanking the hairs out. That, and it always leaves "wounded spiders" in the sink otherwise.) I also use it when I've been working shirtless on hot days - gets the crud off of my chest as well.
Ersatz hand cleaner? Type F transmission fluid, followed by bar soap. The Type F is highly detergent, and will break the crud off.
Out and about? I know this sounds silly, but fine "Hoo-Aahs" field towels. They're actually easier on your skin than you might think, and they're formulated to remove things like camouflage greasepaint (so they work well on grease.) And they don't require water. You can take a whole-body bath using two or three of them!
For getting grease out of my hair, I'll either use Fast Orange (with or without pumice - but usually with. The extra scalp massage feels good...) followed by conventional shampoo, or I'll use some liquid dish soap.
While we're on the subject, I use a paste made of Tide and sand (with enough water to make it a paste) scrubbed in with a stiff brush for cleaning driveway stains, when I work at it. I keep several coin-op boxes of Tide powder around for quick clean-up of the driveway as well. Get it on there straight away, and it works well!