Don't expect to be doing big old dive bombs on a standard strat type trem, it just aint gona happen if tuning is something you care about !

There are a couple of things you can do to help though. One is putting a bit of graphite based lubricant on the saddles and nut (or you can use chapstick). This helps eliminate pent up string tension which is released (slackening the string and altering tuning or use graphtech saddles) when you work the whammy bar.

Another thing is to use locking tuners (like sperzils) which eliminates the need for 8000 turns of string round the peg which is another place pent up tension can lurk.

If you want to do lots of whammying probably the best idea is to get a cheep Kramer with a Floyd Rose trem system or similar. They come in at about 200 bucks from a place like http://www.musicyo.com

best of luck