This is a pretty common problem on guitars that don't have a Floyd Rose style locking nut, you wiggle the bar a tiny bit, and suddenly you're horribly out of tune.
This can be fixed (a bit) by setting up your guitar properly, making sure the strings are all stretched properly, and lubricating the nut. I had the tremolo arm off my strat for 2 years because all it did was detune the damn thing, but I tried rubbing a pencil over the nut so that the graphite went into the grooves and it's improved things tremendously.
It's a pretty common trick, so you might have heard that before, but after trying it I was suitably impressed enough to pass the word on.
Other MAJOR tip[ when dealing with Strat tuning problems is to recognise the effect of string guage on your set-up.
If you change the gauge of strings you use, or even the brand you will have to alter your setup to compensate for variations in string pressure at different points at the bridge.
OTHER STRAT MAINTENANCE TIPS I HAVE LERNT...
If you break a string an have to replace it with another from different set you will notice that your tuning will be absolutely ballsed up until you replace all the other strings with a brand new set.
YOU also have to replace most sets at least every 2-3 months regardless of use.
Put clear nail varnish on your intonation screws (at the back of each saddle) to prevent them popping out due to vibration.
Always make sure that the end-rings from the old strings are out of the saddle holes before putting new strings in.
(this can be a bit fiddly.
Put extra springs into the back of the guitar to help your guitar stay in tune if you have a whammy.
then he told me he needed my guitar and that was grand on my behalf, but on the way down the stairs my guitar dived out of my arms and hit itself of the wall of the stairs and nearly got deaded up but all is still well in the field-ix camp.
am i the only person that takes the whammy bar off and uses it as a drumstick on my strings or as a dj set by hitting and sliding the whammy up and down the fretboard?
Must say I had the problem too with the standard 6 screw strat bridge goin out of tune.They say its better if the inner four screws are loosened off and the out 2 screws acting as the pivot.I put the kahler fulcrum on my strat a long time ago and it cured it.I am tempted to change it back for cosmetics now but I must say I don't beleive it will stay in tune the same without the locking nut etc. Guess I've little faith .
Since I got the set-up sorted on my US std Strat and jumped up a bit from Super light to light gauge strings I haven't had a problem unless you go for a big Jimi dive.
But then tuning up again is part of the act.