Garry,
I know there is a 30 day temporary tag in Ohio:
http://bmv.ohio.gov/fees_for_services.stm that's the fee chart and you can see the fee is $18.50 for a temporary tag. Michigan has 60-day temporary tags as well as 30-day.
The registrar has plenty of contact information (phone and email)
http://bmv.ohio.gov/contact.stm perhaps and email first, I can certainly call them on your behalf if you make no headway via email.
You will certainly need to have the vehicle insured at the minimum; another question to ask is whether or not they need to do something with the title, provided it has one. Let's hope so.
What would be great is if you could find someone to lend you an "in-transit repair plate"; that's how I moved my car from the restorer to home prior to dealing with getting the title (an elaborate process here for an untitled vehicle), insurance and registration. The fee for such a plate in Michigan is pretty cheap, but you have to be an auctioneer or somehow involved in automotive repair or something.
There might also be an in-transit registration for Ohio, that would be a question to ask.