I have removed the Move ability from my Stalker, though it still moves toward a target when I order him to attack it.
Any ways to prevent him from moving at all, but still attack anything in range?

If you have a 'Move' button in his command card, try getting rid of it. If all else fails, make his acceleration/movement speed 0.

Add a buff that sets movement speed to 0 or better suppresses movement?
So basically, behavior: warp prism - make immobile

edit:
use this to disable movement for only a few units. Changing movement speed with triggers might work, too...

Worked.
Thank.

Now, I must leave for work, damn. I thought I'd have the time to finish this little map. XD