Best de-greaser for old caked-on oil/dirt?

Walmart Auto Department. Grab a gallon jug of Super Clean. Comes in a big purple jug. Not to be confused with Purple Power or Crud Cutter although they work too. You can dilute it like crazy and it still kicks ***. If you wash your hands with it straight it may never quit making soap! Buy a good quality spray bottle and dilute it to your needs.
Super Clean. One of the few snake oil products I endorse because I've had good luck with it.
Also Never Seize and Rain-X products.

I agree, awesome stuff! I bought a plastic storage bin and put 2 gallons of Super Clean in and about 6-8 gallons of water. I let the parts sit in it over night and they come out clean(with a little help from the garden hose of course). For engines and big parts, I use it straight from the bottle.