I don't use them, but I've heard good things about Graph tech nuts and saddles for tuning stability.
The saddles aren't very subtle looking mind, don't know if there's any better looking alternatives.
The mastery bridge and tremolo fix all that, i had one on my jazzmaster and its perfection. really expensive upgrade but does exactly what it says on the tin! (i now have to figure out how to gold-plate so i can fit to my blonde JM)
Jags are the coolest...
Really enjoying playing my strat but it goes out of tune really easily, could graphite on the nut and locking tuners be the answer?