I always lightly oil the skillet after each use. I actually put vegetable oil in a spray bottle and give it a squirt or two and then take a paper towel and wipe it on the inside of the pan. It builds up more of non-stick coating so your food doesn't stick. As for the seasoning the outside.... When I first got the skillet, I did oil the whole entire skillet (inside and outside) and then put it in the oven upside down in the oven to season it.... However, I don't oil the outside after every use.
After I clean my cast iron, I always spray a little Pam on it and wipe it in with a paper towel. All my cast iron pans look great. I've got two cast iron pans that I bought about 43 years ago right before my wife came out to join me Newport RI while I was in the Navy. These two pans are still our "go-to" pans for cooking. You can cook anything in them without worrying about it sticking. In fact our kids (hopefully just kidding) always argue with each other about which of them get them after we're gone.
I agree with Great Cook, don't use spray oil! It's fine to use while cooking, but then you need to wash it off! If it drys on it makes it sticky. Just use a paper towel and smear some vegetable oil on it.
I don't oil mine, and I've been cooking in cast iron for 40 years or more. Just wash it by hand with soap and water. Then dry on your kitchen stove burner so it's truly dry. Put it away. As long as it's seasoned well enough, you won't see any rust when you get it out next time. If you do see rust, smear vegetable shortening on it (inside and out), set it on an old pizza pan in the oven or something, and bake it at 300 degrees F or so for a couple of hours. Problem solved.
We just got new Lodge skillets, because I'd foolishly given away the well-seasoned family one my parents gave me 15 years before... because we had new "fancy" pots and pans when we got married. Woe to us! Now we have to season new ones all over again. We are following the directions Lodge provides, to the "T". Although I admit that with the old, well-seasoned one, I used to wash that with soap and water. Now, DH insists we avoid the soap and do just what Lodge says. No idea how my ancestors seasoned that original pan!
I think the people at Lodge ought to start using cast iron cookware, instead of making stuff up. I wouldn't Pam it or oil it once it's seasoned. That is the point of being seasoned. Besides, oil sitting in a pan? Yuck. Nasty. Just use olive oil or something when you go to cook. It's not rocket science. And if you hate my soap and water idea, just clean it with hot water. But dry it on the fire before putting away. It needs to be DRY not oiled.