While I don't recommend eating stale butter, if for some reason you have to eat it, here's my advice:

Melt the butter on a hot temperature in a frying pan. Let the stale smell rise and dissipate. The stuff you cook in that melted butter shouldn't taste stale anymore.

I did something similar to this years ago, with some "stale" butter that had absorbed some refrigerator odors. I heated the 3 sticks in a saucepan, and made a batch of ghee, heating to 280°, which drives off all those aromas that were absorbed, sort of like what you are describing, with a smaller amount. With rancid, that's another matter, and can't be saved.

And to prevent stale butter, what I do now is vacuum seal my butter, when I get it on sale, some in 1/2 lb packs, some in 1 lb packs, and freeze it - lasts forever this way. And in the fridge, I have a widemouth liter mason jar that 4 sticks will fit inside, though usually I only open a 2 pack. Either way, in that glass jar, no odor will creep in, and keeps it good, until I use it.

I've only had butter pick up an odor once.
I went to work in Alaska for 2 weeks and some lettuce rotted in the refrigerator.
I had to toss a lot of stuff.

But normally I keep a stick of butter out so it's soft.
Nothing I hate worse than waiting for butter to get soft.

Or accidentally using salted butter when unsalted is what I'm supposed to use.
Totally messed up a butter cream frosting like this once.

I think our stale butter was already stale when we got it, since it's been in the freezer the whole time we've had it, and it only seems to be a certain kind of it that's stale (the rest of the butter is fine).