Right and left-handed iaidoka wear the sword on their left side. For the initial cut, the sword is in the right hand, BUT, the left hand is JUST (some say more) as important as the right. In iaido, the saya is removed from the blade, not the sword taken from the saya, left and right sides of the body are equally important. My teacher (22 years of practice) asked his Sensei when he first started, if being left-handed would be a disadvantage, Sensei told him that it is an advantage.
btw: the overhead cut is done with both hands, with the left hand providing 80% of the power.