I usually dislodge snow by kicking something: a rock, tree, some ice, or by stomping on a patch of hard ground. Kicking toe first into the snow can dislodge it as well, but often it depends on the type of snow. Using your tool to smack your crampons may work, but it can do damage to both your tool and your crampons, so it's not the best thing to do.
Anti-balling plates are still the best solution. If you're still balling up with your plates on, then you may need new ones, or you may need to treat them to be smooth and slippery again.
I made myself a pair of anti-balling plates that I cut out of a crazy carpet, and they work pretty well:
At first I was just being cheap, but then I discovered that one of the merits of using crazy carpet plates is that they aren't rigid, so the snow can't get packed up inside your crampons as well because the "plate" deforms slightly with each step, dislodging the snow.
The carpet plastic isn't as durable as a solid anti-balling plate, but considering you can get about a dozen pairs out of one $5 carpet, I think you can afford to cycle through a few pairs. I'm still using the first pair I made, and I've been climbing with them a couple of winters now.