Use a bit of fine grit sandpaper. First remove everything from the guitar body, then sand it down till the surface corrosion disappears. Then put a fine layer of lubricant to hinder rust. Vaseline works. Strings should of course be changed out. Be careful when you use sandpaper near pickups, some very fine grades may have magnetic particles which will stick to pups.
A Dunlop CO-101 or a Zorb-it Ci work perfectly to keep rust out forever from a closed case. They work by depositing a fine chemical layer on metal parts. And both work, I'm using them on an acoustic and the only wear on the strings is from playing, not even a spot of rust.
Lee Handmade | Takamine EG-240C | Yamaha Classical | Reynolds beater | Tansen electric | RP300 | Marshall MG30RCD | Behringer Eurorack | E-mu1212M | Delta 66 | lots of other crap