I have light oak cabinets and the one's above the stove are greasy... What can I use to clean them that wont take the varnish off?

Hi!!
My next project is to update the kitchen cabinets. I plan to remove the trim strips, strip the carcases and restain and varnish the face frames. I will construct my own new doors and drawer fronts (perhaps the whole drawer). New hardware, different style doors (more of a craftsman style) and new color should look pretty good.

It is the sides of the cabinets that concern me. I don't think they are even oak. I think the cabinet maker used fir plywood and an oak stain. In any case, they are pretty scroungy looking. They are also not perfectly flat. I am somewhat distrustful of the thin veneers on the market. I can resaw my own veneer and have an 18" Rikon bandsaw for just that purpose. If I were to resaw a bunch of quartersawn oak into 8" wide and 3/32" thick strips, how would I stick them to the sides of the cabinets with any expectation of them staying put. Also, with wide strips of wood over plywood, what do I do about wood movement. Will my thick veneer buckle?

Finally, how do I smooth out the surface of the cabinet to create a flat gluing surface?

So, 4 questions:

1. Should I be so intimidated by the stick on veneers on the market?
2. How would I attach 3/32" veneer to the sides of cabinets without uninstalling them.
3. What about wood movement in thick veneer?
4. How do I create a flat gluing surface.

many thanks,
STEPHEN
P.S. I taught Industrial Arts for 8 years but never certified in woodworking. I was a plastics and metals kind of guy. I did get used to having those wonderful shops around for my own projects and have acquired some tools over the years.

Cabinets are probably 20 yrs. old and seem to have never been cleaned! I'm using Murphy's Oil soap, but there is still "grime" near the handles. I'm afraid I will remove the finish on the doors and don't want another project! This house is 55 yrs old and has plenty of projects already
I have tried Murphy's Oil Soap. The icky grime is still not rubbing off. It must be years of accumulation. I did take the handles off (you don't want to know what those looked like). I don't want to remove the varnish or finish of the cabinets and have a major project on my hands. What is the name of a "degreaser" that you would recommend?
Thanks for the help!

Also, do I need to sand down the varnish that's on there now?

We recently purchased an older home. Built in the 60's. The house is in GREAT shape, but the kitchen cabinets ( lower ones ) have years of food build up on them.. just on the most used cabinets. The cabinets have a great shine to them, and the upper ones look like new, but the bottom ones... another story, and it's just around where the handles are, and a few long drips.. HOW can I save the shine and the cabinets? I want to get the gunk off but don't want to take off the shine ( possibly a varnish ) Please HELP!! I'll need what tools to use and cleaner advice as I've never had to do this before.. I always rented newer homes, and didn't have this problem. Thanks to all that respond.

will varnish destroy the wallpaper boarder?

I stripped all the old paint and varnish off and am down to bare wood (hard wood) I think. I just don't want a too dark of a color which would make the kitchen even smaller. I was thinking pecan or light oak color. Is the all in one ok to use or should I do the step by step method? Room size around 5x15. Very narrow but long

My kitchen cabinets are from the 70's--clear birch with varnish or polyurethane over. I want to paint over them but would prefer to do it without the mess and hassle of sanding. How effective would liquid sandpaper be in this situation? I have been told I need to sand, primer with an oil-based paint, then paint. Any suggestions?

I scrubed down the doors with a TSP solution and fine grit foam sandind blocks. I then rinsed them, wiped them down and allowed them time to air-dry. They are now visible dull but sqeaky clean and smooth to the touch. Are they ready for a primer/paint 2-step procedure? -(Originally clear varnish over stained oak rails and styles with solid luan panels.)

I have kitchen cabinets that were sanded with fine sandpaper , then they were stained to be dark. They also were varnished.I would like to have something that would clean them without destroying the finished varnish. Especially around the stove area where there is some grease build up and then they end up collecting dust. I do not know what to use and keep the original finish and not scratching them also. Thank you for your help.