Hey Jaye, as a certified Strat Cat I feel I can give some pointers in the "how do I keep this $%^& thing in tune" dept.
First off, unless you have some sort of space-age nut, you're gonna need some lube in there. Nut slots like graphite or something like Big Bends Nut Sauce (never tried it, but folks recommend it a lot for this purpose).
Of course, make sure there is no binding going on in the first place. It looks like the plank you are weiding in the pic is at least the American Standard version so I'd be surprised if the nutwork was really shoddy, but you never know. I don't know if you have the trem set up to float at all, but having a good solid setup for your string of choice is obviously step #1. I have my bridges set up so I can pull up a fair bit, too, and that is part of the method I use to tune the dang things and get them to stay there.
First off, tune each string bringing it up in pitch to your target. Then, take the whammy bar and depress it so the strings go nearly flat against the fingerboard. Let 'em back up and see where the pitch is. If you have gone sharp, try pulling the bar up and see if it gets you back in tune. If this action gets you back in tune, you're almost there. If not, try doing a whole-step bend and see if you drop back down to tuned. What you are trying to do is find the balance point where any sharpness due to diving or bending can be quickly "pulled" back in to tune. You end up tuning, dive-bombing, pulling up and starting all over again until it staays pretty well in tune no matter how abusive you get. Often times you have to tune a hair flat, do the drop, and it will jump up into proper tuning. I have had great luck keeping most of my Strats in tune this way, with the exception of my Jeff Beck, but that has a special (PITA) roller nut that I suspect is more trouble than it's worth.
It might seem like a silly ritual, but with a little time and some proper setup and maintenance a traditional Strat trem can be made to stay pretty well in tune unless you are being radical. You should be able to grab the arm and do very wide vibrato stuff and not budge a bit out of tune. Or, there is always the Floyd Rose system /emoticons/default_biggrin.png Let me know if you need any help getting that thing dialed in. They are well worth the effort! Love the color choice, too.
Z