DO NOT bake on an old sticky finish!
Most likely it won't bake hard anyway - and if it wasn't baked on to a nice hard finish, it's probably rancid. I wouldn't want to eat off it and it would probably make the food taste bad.
If you can, wash your sticky cast iron with a bit of soap (yes, I said soap - it cuts the grease) and HOT water. or you can try just alot of hot water - but you gotta get the sticky stuff off. Once you have all that sticky old grease off, you can dry your Cast iron in the oven and re-season. If all else fails, you can put your Cast iron in the self-cleaning cycle of your oven - but be prepared to smoke up your house.
I know I'll probably get flak for this - but soap is not bad for Cast Iron - it's just that it can
take your finish off if you let it. If you use a bit too much, or don't rinse it all away, it can
flavor your food with soap taste. But a tiny bit of soap won't hurt a really good hard-baked finish if used in moderation.
if you have a good baked on finish, and clean your cast iron after each use and DRY IT THOUROUGHLY you should not have to oil it between uses. Esp if you don't use your cast iron everyday - you shouldn't leave oil on it as it WILL turn rancid. Do not store your cast iron in a garage or shed - especially thru a winter - the cold makes humidity condense on it and causes rust. Store it somewhere that it is not exposed to extremes of temperature.
there are many ways, types of oil, etc to properly season cast iron. My only recommendation is to NOT use olive oil - as it burns more easily at high temps. use something that can take 450-500 degrees.
this is what I prefer - Starting with a clean dry piece of cast iron - pre-heat your home oven to 450-500 degrees. Place a piece of tinfoil on the bottom of the oven to catch any drips. Using a paper towel or clean rag, put a THIN, THIN
coat of oil on every surface of the cast iron - inside, outside, lid, handles, etc. place the DO in the oven upside down, along with the lid, so that any extra oil will drip away, not pool in the bottom. ( that's what the foil is for) Most 'sticky' DO's happen because the oil was too thick, or the oven not hot enough to really bake it in. Many new to DO's think
they've used a thin coat, when they've really used too much. ( this was my mistake when I started) leave the oven on for an hour or so, then turn it off and let it cool down with the DO inside.
ideally, two or three coats like this should give you a hard, shiny, finish that works much like the best Silverstone. ( except that you CAN use metal utensils on it!
If you don't want to do two or three coats like this - do ONE, then USE your DO and fry up some hamburger, sausage, bacon or other greasy food. after cooking, wipe your DO clean ( no soap, no water if you can help it) and turn it upside down and leave it in a hot oven ( pre - heat and then turn off) again. Some folks like to cook some onions in oil - they say it gives a bit of flavor and helps spread the oil. you can do this over a number of days - once the first coat is on, no matter how thin - you've protected the DO from rust.
the best way to get a really good finish is to USE your cast iron!
However you do it ( and there are MANY ways that work) the thing to keep in mind is that when your oven is clean and ready to be put away, you should be able to wipe it with a towel and not have it come away greasy, smokey or stained. your hands should not feel greasy when handling the cast iron. your 'finish' should be hard, shiny and smooth to the touch. when cooking, food - even eggs - should come away easily - (unless you burned them).
After I cook in my cast iron, i wash it right away, (sometimes with a bit of soap if the food was really greasy) rinse in HOT water, and then I'll put it on a flame on the stove or back in the fire for a few min. That way I'm sure ALL moisture is baked out of the iron. Often I will wipe down the cast iron with a bit of oil on a paper towel - esp the food surfaces - to keep my slick finish - but I bake this layer dry on the stovetop or coals before putting the cast iron away. you can watch the cast iron on the stove and see when it heat dries the oil on - it kinda turns from a 'wet shine' to a 'dry, textured shine' as it bakes on. Let the pan cool completely and then put it away.