Cast iron care need not seem so intimidating or mystical. There are lots of ways to take care of it, and though many will profess their own gospel and taboos associated with cast iron cookware, many different solutions will work. You just need to understand some of the basic principles and the rest is personal preference.
First, in my naivete I used vegatable oil as the seasoning
There is nothing wrong with using vegetable oil as your seasoning. That is often what you will be cooking with anyway, and every time you cook with oil you are contributing to the seasoning on your skillet - so obviously it is a fine type of oil to constitute your seasoning.
second, I also didn't remove the excess oil, leaving a sticky and uneven finish.
This has happened to me a number of times, even after removing excess oil. When you season it in an oven (preferably upside down), the oil heats up which can often cause it to run more easily before it has a chance to bond to the iron. That can cause it to leave spots without seasoning, and the spots that are seasoned will sometimes be sticky. I would just repeat the process again until the surface is completely seasoned. I usually wipe a light layer of vegetable oil on mine, turn it upside down in the oven, and bake it for an hour or two at around 350°F with a cookie sheet under it. It'll probably smoke a little bit, but don't worry about it.
Additionally, when I break in a new cast iron whatever, I like to cook with really greasy and oily foods (like bacon) the first few times I use it. It will help create a better seasoning and get rid of those sticky spots. Really let it pool up and try to cook for a decent amount of time. That can help get a nice, uniform finish on it. Scrape it clean with a lightly abrasive sponge or nylon brush and rinse it in cold water (maybe a tiny amount of dish soap if you really want, but it honestly doesn't need it). Dry off. Cook on it again. The more you cook with it, the better the seasoning will get.
Looking at your pictures, I would not do anything so drastic as use a caustic cleaning chemical to strip the seasoning off and start over. Just scrub it nice and clean with some soap, dry it off, and try seasoning it again. And again if you are still not satisfied. You'll get there.