#1
I had my guitar modded by a professional for Christmas. I have a Fender Standard MIM Strat, and I had two Bare Knuckles pickups installed (AWESOME!), a Fender LSR Roller Nut, Fender Schaller Locking Tuners, and Graph Tech String Saver Saddles. And yet somehow, the guitar still goes out of tune almost as easy as it did before. I can only think that it could be I took the strings off of the string tree (I'm almost certain the tuners are staggered (the ones I bought are http://accessories.musiciansfriend.com/product/Fender-Schaller-Locking-Tuners?sku=361333)), or that the bridge is still a standard MIM bridge, or maybe intonation and the fact everything is still new and on the first set of strings. I'm not sure, though. Help, please?!
#2
New strings will definitely stretch. The fastest way to stretch them and see if they're the cause, is to loosen them up. Remove the tension on them by using the tuners, then stretch the strings. Retighten them to concert pitch and see if they still go out-of-tune. If they're still going out-of-tune after a few days, then I'd suspect that something else is causing the problem.
#3
As he said, stretch the strings very well.

Make sure you're locking the tuners, and that the strings are moving properly through the nut when you use the trem.

Also, did you get rid of the string tree entirely? Use them, they ensure proper string tension over the nut, so the strings don't get all floppy and losoe and pop out.
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#4
Well, I haven't been using it because I'm getting Graph Tech string trees this week (they came late,) but I did have the string tree on when I got it back, and the tuning didn't get any better when I took the strings off the tree (its still on the guitar, FYI.) And I've played it and used the tremolo a lot and have been doing bends and stuff, so the strings are probably stretched alright, even I'm stretching them now. Does that mean that it's the bridge?