I use duel wielding only... OFFENSE, OFFENSE, OFFENSE!!!!
I also noticed my Strength stats change when using close combat weapons... Is that determined by the Warrior class I picked?
Not that I know, but maybe one (or both,) of your melee weapons give a boost to strength? did you put maybe a Strength Charm on the weapon(s) ?
Choose to be a Warrior if you left Farglow give you 4 points in Strength, but I think you know that already ...