How do I repaint the kitchen Cabinets ?

https://www.wikihow.com/Remove-Oil-from-Wood

http://www.howtocleanstuff.net/how-to-remove-oil-stains-from-wood/

https://www.hunker.com/13422976/how-to-remove-an-oil-stain-from-wood

https://tips.simplygoodstuff.com/remove-greasy-buildup-wood-cabinets/

Have you tried a degreaser? I use Dollar Tree Awesome Degreaser (as does our local car detailer)

If that doesn't work then I would use paint stripper like Kleen-Strip, it will take off anything.

Clean with TSP, trisodium phosphate or Krud Cutter.

Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 220 grit sandpaper or a green Scotch Brite pad.. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like Zinsser 123, KILZ,or BIN and have it tinted to the color of the top coat. This will prevent dark or stained surfaces from showing through the top coat. Acrylic, or water base paints are low-fume and clean up easily with water. Alkyd, or oil-base, paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.

Yes get as clean as possible, prime with Kilz, paint with 2 coats of oil based paint. Do not apply poly on top. Not needed and can cause peeling.