Of course you can. Future owners of the house will swear at you to no end, but that's their problem, right? ;)
There are two critical steps in prepping kitchen walls.
Clean and degloss
Cleaning is critical: TSP or TSP substitute.
Deglossing: either light sanding (120 grit) or a chemical deglosser
Once a surface is deglossed, it should be primed, especially if going from one paint type to another.
A deglossed oil undercoat can be primed with a latex primer. Either oil or latex can then be used as a topcoat.
A deglossed oil undercoat can be primed with a oil primer. Either oil or latex can then be used as a topcoat.
It is better to stick within families of paint types, if you can, but going back and forth between types is possible with primers.
At this stage in coating, I'd let everything dry for a week, then sand lightly. If the previous layers are adhering, then proceed with latex primer, latex topcoat.
If,, however, they are sloughing or chipping or you can easily pull a layer off if you leave painters tape on overnight (and then pull it off), then you must sand down to the last well adhered layer and then repaint. Good luck.
Best Answer
Stripping or sanding existing paint off of a wall isn't done unless the paint is really bubbling or chipping off.
For painting walls, the best way to go is to clean the walls, put on a coat of primer, and then finish with 1-2 coats of a latex paint.
Primer will cover an oil or latex paint and give the new paint a uniform layer to adhere to. This is good because you say that the wall might need patching. The patched area and the original walls will take paint differently and could end up with a different sheen if you do not prime first.
Now, this could be somewhat region specific, but I don't think so. Interior walls are normally painted with a latex based paint. High traffic areas will use a glossier paint to make it easier to clean (bathrooms, kitchens), and bedrooms normally use a flat, non-gloss finish. Oil-based paint is still used in limited application for trim, but really most of that is also latex.