So I'm sure we all know how to remove a set of strings but an easy tip is to quickly snip them off with a wire cutters. There's no need to save the rusty, smelly old strings so we might as well make life easier and take them off the fast and easy way.
When it comes to removing rust or oxidation I recommend a "fine" or "extra fine" piece of steal wool. These labels will be displayed on the package and you can get steel wool at any hardware store.
I've found that this process works better on bridges but can be difficult to accomplish on pickups since there is plastic involved.
When using the steel wool, be aware that our pickups are magnets. That means the steel wool fibers will stick to them. I always make sure to blow of the remaining fibers. (be sure to close your eyes if you don't want steel wool in them)