I have a problem tunning my guitar that has been buggin me for a long time. Any time I change the tunning of one string it messes up the tunning of the other strings. So, let's say if I went from standard to drop D all the other strings would be out of tune. My guitar is a mexican strat if any one can help.
thats just what happens when you have a tremolo. the tension gets messed up for the other strings when you tighten/loosen one string, its pretty normal.
The Gear:

Custom Strat
Mesa Boogie Stiletto Ace
Fulltone OCD
Electro Harmonix Small Clone Chorus
Dunlop Crybaby Classic
MXR EVH-117 Flanger
Fulltone Soul Bender
i have a mex strat too and also had that problem. after a while i decided i dont need the automatic-string-detuning-device/tremolo and adjusted the strings in the back so the bridge touched the body and didnt float anymore. works great.
but if you dont wanna sacrifice your trem, i hav no idea...
Ibanez K7
JCM 800
the first thing i would look for is whether or not your tremelo has enough tension. do you do a lot of whammey bar stuff? make sure the trem bar doesn't move too freely. some people set strats up by loosening the screws holding the bridge plate on to make the trem bar easier to use, that can mess with tuning. if that isnt the case try adding or tightening the existing springs in the back of your guitar.

sometimes old strings get really unstable. you could try changing your strings. new strings are unstable, too. try pulling up on your strings pretty hard to get rid of some of the slack when you change strings. but it sounds like this happens no matter what strings are on.

if not, it could be that you need to get your neck adjusted. i wouldn't recomend that to a beginner... well, anyone who hasnt done it on someone elses guitar a few times first. haha. dont ruin your neck.

finally. mexican strats are pretty cheap. i have to adjust the tunings on my more expensive guitars pretty regularly. it might just be that your guitar is fine, but you have to tune it once in a while.

hope that was helpful.
to change tunings on a floating bridge like you describe you'd have to get the whole bridge reset, drop d would create a different balance and effect the other strings. its a bitch i know, hate not having drop d anymore...