Well, you got a mess there. I'd start by physically removing everything that I could like Joset said and scraping out as much grease as I could. Then I'd get some kerosene, q-tips, rags, tooth brushes, and a cat litter tray. Put the machine in the tray and start cleaning. Let the tray catch what drains down. Use a hair dryer to soften it up if needed.
You might also try Hoppe's #9 gun cleaning solvent. It's mostly kerosene and will do a decent job of cleaning off the grease.
Good luck in your clean up. And I hope someone offers a better idea.
Joe