Weapon skill stats and accuracy contribute to weapon accuracy. I can't find the page with the relevant equations on, but rather than calculating a "to hit percentage", the game calculates a Gaussian distribution, and places the shots according to that. One of the bits of the equation is (weapon_skill + accuracy)/200, so a "perfect" shot requires a total of 200 points between the two
Strength does not (yet) do anything, but an item weight / encumberance system is planned for eventual inclusion, I think
Speed affects your TUs per turn
Mind affects Morale, and soldier promotions. It also seems probable that it will be used in the psionics system, when that gets implemeted. It might get renamed though