An Overdrive Finish comes from winning a round with a Distortion Drive or Exceed Accel while in Overdrive Mode.
Considering Overdrive doesn't last very long I found the easiest way to do this was using Exceed Accel.
I changed L2 to be all 4 buttons (A + B + C + D) to activate Overdrive. Once the opponent was low on health I would hold down L2. This would activate Overdrive mode and then go right into the Exceed Accel. There is some Invulnerability frames with the Exceed Accel and I would often hit the opponent while they were attacking me.
You can also do this is vs mode with 2 controllers.