Just two days ago, my Omnia started behaving normally again. Weird. My phone is company-owned, and they won't give me a new one because the Omnia is out of warranty, and I'm not due for an upgraded from VZ until August.
So their option was to give me a used blackberry. I chose to stick with the Omnia, and carry around a portable charging pack until August.
Along the "battery" theory, I have gotten occassional messages about the phone not recognizing the battery and saying it's a third party battery, or something like that. But it's the stock battery from day 1. Maybe if it starts acting up again I'll replace the battery- unless it's really close to August!