*cough* I was once a member of the law enforcement community...not all of them are jerks (just most...lol).
Honestly, and I'm *not* defending this cop in this case at all (in fact, I would've been reamed for handling an arrest like that...and would've deserved it), but I think many cops out there are just doing their very unpopular job. I always used to joke about how everyone hated us until they needed us...we were heroes for five minutes, but after that, resume the hate. Anyway, I digress...
Definitely talk to a lawyer about this. I personally question any law that assumes guilt in the absence of correspondence and wonder if it would hold up in a higher court, but I'm certainly no lawyer and my former employment was simply to enforce the law as it was written, not interpret it. It just appears to fly in the face of any presumption of innocence.
One thing that may work against you is if you failed to change your address on your license within the required time period after moving, which subsequently led to you never receiving the notices (if that comes out, be prepared to have more charges added to the case...I've nearly been bitten by that one myself). Also, I have no clue about Ohio, but in some other states and jurisdictions, the decision to impound vehicles is often left to the arresting officer. Personally, I wouldn't have impounded it since you probably had someone that could retrieve the vehicle and move it from where it was in relatively short order. The only times that I would choose to impound a vehicle is if I believed that it would be unlawfully operated within 24 hours or if it were obstructing traffic or access (there is a third reason as well: high probability that your property would be damaged or stolen at the current location...departmental liability in that case if I didn't have it towed). Some cops are jerks, though, and want to maximise how much time and money you need to spend in order to go back to your daily routine, so they tow absolutely everything.
I really hope this works out in your favour and am saddened to hear stories like this, especially from honest, hard-working folks. Hopefully you'll find some good representation and get out of this mess with minimal cost or impact to you in the long run. Ideally, I'd love to see laws like that one get overturned in a higher court, but that's a lengthy (and sometimes costly) prospect that few are willing to undertake.