I know what you're talking about, I get the same thing on my strat. I've never experienced it on any of my other guitars though, and my ibanez guitars never had that problem for sure...

On the strings, wash your hands before you play, and maybe just get into changing strings more often. On my main guitar, I probably change them about every 2 weeks.... there is a brand of string that are rust resistant as well - 'Elixir Nanoweb'.... They cost more, but apparently last longer (I've not used them myself though).