I'm not sure whether or not the skills you get with your character have specific hotkeys.  If they don't, they really ought to.  I imagine, however, that they must have hotkeys.  It would be a rather large oversight if they simply did not.  The reason I don't know for sure is because the tooltips for the skills don't list what the hotkeys for the skill is.  This should be changed.

Each skill should have an intuitive hotkey associated with it.  For instance, a skill named "Fireball" would have the hotkey "F", or perhaps "E" or "R".  Any key near the left hand that isn't used for other things already.  Since all Demigods have different skills (duh) you would only need a certain number of unique keys for each one.

Alternatively, you could simply implement something akin to an MMO hotbar.  The player drags and drops things to the hotbar - potions, skills, items, etc - and uses a corresponding number key to use / activate them.  So I put Fireball in hotbar box 1 and I press 1 in order to use that skill.