General Discussion
Was looking through the GM Guide and the Ultimate Edition on the rule for Supernatural Strength using melee weapons and they did properly clarify that (though the two books say slightly different things); check page 26 in GM Guide and pg 286 in the Ultimate.
The gist of it is that when using a melee weapon Sup.Str people use the higher of a) The weapon damage + character hth dmg bonus, or b) Supernatural Strength punch damage (+hth damage bonus? GM says yes, but Ultimate doesn't). I don't think this would apply to energy blades/wpns as their damage comes from the energy form versus strength.
This seems like a fairly decent way to handle it and would give supernatural character/creatures a reason to use an MDC weapon (in some cases) over their fists or claws. Since a fair number of supernatural strength persons have pretty high PS values they would be adding a good amount to damage rolls, which may tip the balance in favour of weapon use.
Example: Mika has +20 to damage, with her magical Dwarven longsword she would do 1D8+4+20; max 32! That's compared to her punching (4D6), so it makes sense for her to use such a weapon.
The downside is that if you're not using a magic weapon there's a chance you'll break it; 30% chance if you do more than 3x max damage, or x5 max damage for mastercraft weapons.
I'm sort of inclined to go with the Ultimate Edition rules as it doesn't make total sense that you could elect to do your supernatural punch damage plus hth dmg bonus. Seems like a cheap way for REALLY strong characters to do extra damage simply from picking up a 1d6 magic dagger.
