Where does your damage come from in the unarmed skill? The game I think says it's from your STR but wiki says that STR does not effect unarmed damage...anyone know?

Endurance and Strength both.

It affects the skill which in turn affects the damage. It used to be that in the old fallouts that strength would add to a bonus to your melee damage as skill != damage but skill = chance of success.

No, Strength have nothing to do with Unarmed.

well except for being able to carry a ballistic fist.