Is there any way to salvage an old rusted wok?
Hi Leigh Anne and welcome to Seasoned Advice! First let me say that you will probably get a few different answers as many of us have different ways of handling such issues.

Since you had what sounded like a pretty good amount of rust to start with, I would recommend a thorough cleaning with steel wool to ensure that you have removed all of the rust. Be sure to rinse well and dry thoroughly.

Regarding the type of oil, I would recommend a good quality vegetable oil. You could also use a good quality vegetable shortening. Make sure to apply a very thin layer and wipe off any excess, especially since you are not using the wok frequently. Any excess residue can become sticky or gunky when the pan is left to sit for a period.

As for gas burner or oven, that is really your choice. I personally would use a gas burner but many prefer using the oven.

All in all, it sounds like you already have a pretty good handle on this. A couple of other things you may want to consider, though. Even though you are keeping the pan in the open air, humidity may be a factor. Also, if you live near a body of salt water, salt in the air could be a problem. You may want to consider keeping the wok in a closed plastic bag. (I do this with any cookware that hangs or sits outside of the cabinet to ensure it's always clean and dust-free when I am ready to use it.)

Good luck! :)