Sailfish, No, you don't need to be worried. What happens is that, during heating, the oil changes, and the molecules in it start linking together into long chains. These polymerized oils seem tacky, but generally they're pretty nonstick. Another way of getting rid of them is to simply bake the pan at relatively high heat. Oils are made up of hydrogen, oxygen, and carbon atoms. IIRC, when you start to heat them, you start driving off hydrogen and oxygen atoms, leaving free bonding points on the molecules, which then start clumping together. If you continue to bake an oil at moderate heat (350 to 375), you'll finally drive off all of the hydrogen and oxygen atoms, leaving a fine layer of carbon atoms behind. That is the process by which you "season" a cast iron frying pan to achieve a very durable non stick surface. That layer of carbon atoms is your friend.

Just tyi, the sticky residue is I think because you left it on too long and it dried. You want to remove the stripper when it's still wet. If you have a lot of old layers of paint, put the stripper on thick and cover it with plastic and remove it the next day. The plastic will keep the stripper from drying out.

Oil buildup on cabinet finishes damages them over time. Oil soap is one of the worst contributors to that. So is poor ventilation that allows grease particles to float around the kitchen. And knobs and pulls that don't have enough projection to them. Try mineral spirits on one of the back side of the doors to make sure it doesn't damage the finish (it shouldn't) and then use that to clean around the knobs. If the other conditions that I outlined above are present, then you may see continued deterioration of the finish. You should see about addressing kitchen ventilation and possibly your knobs. Oil soap has already probably done it's damage though.

Thanks, lukki. Unfortunately, I have an area approximately 11' X 4' to deal with. If it was only a strip of residue, left from something like a long piece of tape, I'd attempt the process outlined in the article you linked. Since it's such a large area, I'm a little apprehensive. Today, the amount of 'stickiness' seems to have lessened. I'm still considering calling a place like Stanley Steamer to see what they have to say about my situation. We do have another room (or two) of carpeting that needs to be cleaned, so it may be worth my while to just have it handled when I have the other rooms cleaned. Perhaps this is the incentive I've needed to get all the carpeting cleaning done.