I don't have really greasy eyelids but you can try some of my own tips:

Use a good base for your eye shadows. UDPP is a must have for all make up lovers! It makes your eyes shadow stay on longer and not crease. I'm not sure how well they will work if you have really greasy eyelids though.

Also, I dab a little bit of press powder on my eyelids before and after I put on eyeliner so that it doesn't smudge.

For eye liner, try gel liner (eg. Mac Fluidline).. that stuff doesn't budge!