According to Stoneslings.com, there are two methods of releasing the slingstone/shot from the sling. They are:
RELEASE 1 (Underhanded): After loading the sling as described above, swing the sling FORWARD as in fast-pitch softball. Your arm should be moving at the shoulder, not at the wrist-- the cords are an extension of your arm, and you are making a large, somewhat diagonal circle in the air. Practice releasing your thumb at the moment when the projectile will leave at a 45 degree angle. You can even get a running start with this method. This type of swing is great for power and distance--lobbing. It lacks accuracy though.
RELEASE 2 (Over the Head): This method starts as the first-- underhanded and forward. But, as the sling is swirling, bring it over your head, your arm turning more at the elbow than the shoulder. The circle over your head should be about perpendicular with your body. Again the sling cords are extensions of your arm. This time, however, you throw like a baseball. Throw your arm like you would if you were throwing a baseball but only when the pouch is swinging forward--add the strength of your arm to its momentum. Practice to get a feel for the release point. You'll feel less power with this method, but the accuracy will be up.
Note that the second method specifically mentions that you are adding the strength of your arm to the momentum of the shot (though I think both methods would use strength as an element).
I have (tried) to use a sling once before. Let's just say I was not sucessful, and suffered a minor injury in the process...however those who were able to use the sling did seem to cause more damage (to a cardboard wall) if they were stronger. It seemed to me that the shot will go farther, and hit harder, if you are stronger. It's similar to a baseball - if you thrust forward harder, the shot will fly harder.
I think if reality were important to the sling rules (which it isn't necessarily) that dex should determine your attack modifier, but strength should determine your damage modifier. I also think it should be treated as a thrown weapon for purposes of the halfling thrown weapon bonus.