#1
Would they actually help my strat stat in tune? Note that I have one of those standard vintage trems, not a Floyd Rose or anything.
Gear:
Schecter Hellraiser Deluxe
Boss DS-1
Crate GTD65

GAS List:
Mesa Boogie Dual Rectifier Roadster
#2
Yes, they will, but adding a graphite nut will also help more. While locking tuners improve tuning stability quite well (look at John Petrucci's guitars for proof), they're not quite as perfect as a Floyd Rose. Luckily, a graphite nut won't set you back too much either

But adding locking tuners will definitely improve your tuning stability, no matter which way you look at it.
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#3
Thanks!
Gear:
Schecter Hellraiser Deluxe
Boss DS-1
Crate GTD65

GAS List:
Mesa Boogie Dual Rectifier Roadster
#4
There's other things you can do before you buy locking tuners.

Check out my little guide:

There's several factors, when you're trying to keep a guitar in tune:
- Stringing technique
- proper setup
- As little friction as possible.

So let's attack these possible problems.
Friction - Your guitar has what are called string trees:

The circled metal thing keeps the string from popping out of the string nut. Useful, but they also create friction that prevents the string from returning to its proper pitch after a bend or something. So...apply some sort of lubrication to to the underside of the string tree, as pointed to by the arrow. Use something like Big Bends Nut Sauce, or Guitar Grease. Even pencil lead will work. Simply grind the pencil lead into dust on a paper, and use some of this dust on the point of friction. You can even use machine oil.
The same problem occurs at the string nut. Each groove has a bit of friction. So you can apply the same lubricant there, underneath the string, and that will help. You can also buy the appropriate replacement nut, but the nut should be made of graphite. There's less friction from that material.

Moving on to setup. There's a lot of material to cover with setup, far more than I feel inclined to go into...but I can point you towards some helpful links:
http://www.projectguitar.com/tut/tutorial1.htm
https://www.ultimate-guitar.com/forum/showthread.php?t=602241&page=1&pp=20

Lastly, stringing technique. Yes, it's possible to string a guitar improperly. I actually mess with my Strats trem a lot, and it stays in tune really nicely. Of course, I have it lubricated at the proper points of friction and have a graphite nut, but I don't use locking tuners or anything like that. The secret? Stringing your guitar the right way! Here's a link that will show you how I do it:
http://www.stringthis.com/howtostringu.html
#5
You could replace the string trees with graphite ones as well as the nut + locking tuners = stability heaven.


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#6
on my strat what ive done is have 3 springs
graphite nut
graphite saddles
locking tuners
and a new bridge is coming soon too

tuning stability is amazing
#7
Yeah, I'll lubricate all my string trees and stuff and string it the right way, but instead of spending $60 on locking tuners I'll just buy a new guitar.
Gear:
Schecter Hellraiser Deluxe
Boss DS-1
Crate GTD65

GAS List:
Mesa Boogie Dual Rectifier Roadster