If the outdoor hot fire method does not work, you can also use oven cleaner. I had an over-100-year old antique cast iron pan that was rusted and had burned stuff on the bottom. (It was my dad's and given to him by my oldest uncle who had gotten it from his grandfather.) I used about ten coats of oven cleaner and took it down to "grey metal" or the way it looked when the iron was poured into a mold and cooled. I would heat it in the oven and then coat it with oven cleaner. It took maybe ten coats to get off the rust and all the baked-on oil gunk that had accumulated over the years. Most of the bottom of my old pan was covered with crusty stuff (burned oil or fat) that would not come off with regular scrubbing or even soaking. You can even use steel wool to remove rust. My last step before re-seasoning was to bake it in my self-cleaning oven until it was back to grey metal.
Then, I had to start the re-seasoning process from scratch, but when I was done, it was gorgeous, and all the crusty black stuff on the bottom was gone and you could clearly read the lettering. I have a smaller old pan my aunt gave me which is rusted and one of these days when i can work outdoors, I am going to treat it with oven cleaner and use steel wool to get rid of the rust.
Beware that there is a lot of controversy about what kind of oil you should use to season your pan. Some of the vegetable oils will turn rancid, especially if the layer is too thick and if it is not used very often. Here is a website by Lodge, the maker of most of the really good, old stuff.
http://www.lodgemfg.com/use-and-care/what-is-seasoning It says they use soybean oil. You also might want to store the lid separately in the future and make sure the pan is thoroughly dry before you store it. I remember my mother wrapping this one in old feed sacks, which were 100% cotton. (I finally tossed out the last of my collection of horse feed sacks when I sold my condo. Unfortunately, my mother had very carefully bleached off almost all the pictures of horses on them, or they would have been frame-able!)
Since I had not used mine much in the last few years, I gave it to my niece and her brother to fight over. My nephew and my niece's husband went to culinary arts school, so I knew they would appreciate it, as compared to my kids who thought I ought to just buy a new pan!