It's been a while since I've spoken to them, so I checked my Journal. Craig, Domingo, Oscar and Karakos (but he's inside where the Don is) are able to make you stronger.
I tend to use Craig, he's the red haired guy that arranges arena matches. After a short conversation with him about betting and the arena, he'll teach you 1H sword and Strength.
Thanks, Oscar has not offered Strength training and Domingo won't talk to me. I've said little to Craig cause I never 'bet'. I'll explore that line of dialogue and see what develops.