What kind of cleaner can I use on wooden doors?

There are wet wipes that are made especially for wood. Pledge is a known brand and I use them in my house. If you prefer organic products there is one too. I cannot remember the name right now but I have that too. Target stores carry them, do you have one in your area?

Definitely avoid any cleaner containing amonia (like window cleaner and some others). The amonia can eat away at the finish...even if a test patch looks ok it could still cause damage that will add up over time. I like using water and dish soap for things like that. Murphey's Oil is also really good for protecting and cleaning wood surfaces.

murphy's cut with water works pretty well on any wood.it's never damaged the surface of anything in my house,and it's even better on floors.

A vinegar and water mixture is harmless to just about everything. Try that on a small spot. 1 part vinegar to 3 parts water should do it.

I would think that you could use a spray cleaner. I would use a test patch first though.