If the umpire determines that the ball hitting the bat was not from an intentional action of the batter, it's still live.
It's up to the umpire to determine if the ODB touching the ball hindered a play on it (seems like a stretch here, but you'd have to be there). If he determines it to be interference, he then has to determine where the runners were at the time of the interference. If they had legally made the next base, then they stay there. If they were not there yet, they have to go back (no matter how close they were).