I have an old ax head that I soaked in vinegar and salt to remove the outer layers of rust. That worked just fine, but after I removed all of the rust and let it sit while I shopped for a new handle. After about a week there is a new thin layer of rust that came back. I live in Florida so tools rust quite often. Should I put mineral oil or some other kind of oil on there? I've also read that butchers wax can help as well. Any advice would be greatly appreciated.
I've used water displacers like WD-40 (or Jig-A-Loo -- whatever is on sale) to coat saws and such (I'm in SW Ontario, parts of which are basically the middle of a swamp in the summer) with good results. Just a thin coat and rub with a cloth. For longer term storage I've been known to wrap tools in home-made "oil cloth" which is basically a cotton t-shirt thinly coated with WD-40.
My fine woodworking tools (i.e., those tools that might stain some of the prettier projects if I coated them in any oil) are stored in a separate toolbox with handfuls of those silica gel pouches I've saved over the years. You can buy silica gel, of course, but I'm too cheap.
I've never used it, but there is at least one Floridian Youtuber who uses "Evapo-Rust" sealants after refurbishing metal tools. Now, Evapo-Rust, as a brand, is very keen on getting their products seen on Youtube, so a lot of those sightings are because they aggressively sponsor YT channels. So, your kilometerage may vary.
If you are less than 20 miles from any salt water ,rust protection is a challenge. Not to be repetitive but oil, any oil, applied repeatedly as needed will give good protection. Very long ago , refineries used wax on storage tanks; Not because it is better than oil but because they had it as a byproduct. Next time you clean off rust try "navel jelly" , aka - conversion coating . Phosphoric acid removes oxide and leaves a slightly protective coating of iron phosphate.
I'm in the mid-South. Lots of humidity here. Rust speed and amount always varies by metal. In my shop, I keep automotive carnauba wax on metal surfaces fairly often. Cheap, easy, doesn't stain wood.
Also, for some older tools I've restored, I used gun bluing and I actually like the look. Obviously, bluing isn't a complete rust stop, but it is better than nothing. For some tools and surfaces in my shop, that are constantly getting used (or covered in sawdust!), there's rarely call for any additional protection.
Just my opinion.