Wow, I have been there once or twice on contracted paint jobs. This is a mess and if ever contracted to do this again, I will insist on the homeowners do the cleaning. This was no doubt more work than the painting itself.
First, remember, you cannot prime or paint until all this stuff is off. I mean OFF.
I was in a home with owners that did not want any chemicals used so I resorted to a product called Simple Green and I'll be darned, it did do a good job. Although 409 and others would have worked I imagine.
Your first attack should be with a mixture of water and vinegar, heavy on the vinegar, this will cut the grease.
After you think that your done, then use a very good primer that does the best job on this environment:: Zinzer B-I-N. This is stronger than Kilz and Kilz 2. Apply many coats and allow each coat to dry properly. Keep applying coats until the stuff does not leave a shadow.
Should not be any more than two coats.
You should be ready to go.
remember use a good quality of paint, not from a home center or hardware store. A good quality, if not, you will have wasted all your work and money.