I think I've at least partially cracked this. Damage is a seemingly flat range between a min and max value, determined by
Min damage = Power
Max damage = Power + MIN(Power, Stat)
Power is just the base power of the technique plus modifiers.
There might be some additional effect at play; I haven't looked much at higher powers except to see that it seems to fit this formula. I also never noticed any difference from monster to monster, but there are probably some monsters with special defenses. All spading was done against monsters in Southside Park, mostly while non-etheric. (So gangers and 3rd eye gangers.)
In the best case scenario raising your power adds 1.5 average damage, worst case it adds +1.
Raising your stat adds at best +0.5 avg damage, but for low power techniques won't help at all.