Well the Oni bonus isn't any different from any Ork picking up the "In Training" perk. In fact, it's identical. The problem being that unless you use your hand on your own obstacle you're going to be out of cards REALLY fast.
I'm not sure I understand what you're saying, and so I just want to check that you are playing right.
If you don't play down to below 3 cards in hand, you won't draw at all. If you do play down to 3 cards or lower, you'll have a discard pile, and when you draw from your deck, after you draw the 1 remaining card, you'll shuffle up your discard pile to make a new deck. It's really hard to run out of cards to draw.
Also, it seems to me that you would get the same result in terms of drawing cards if you attack an obstacle in front of another player, as if you attack one in front of yourself.