"Is there not a statute of limitations for this ?"
If you were convicted and part of getting your license back and keeping it was the class: no. The SOL only applies to bringing charges not to completing the requirements for the court and DMV.
"Is there a reciprocal agreement between Ohio and Delaware?"
Yes, it is called the Interstate Driver's License Compact. States that participate share their information with a national database and honor the suspension, revocation, and license requirements of other states. So when DE suspended your license for not paying the fine and attending class; when OH eventually caught up with it they honored it too under the DLC.
"The whole thing seems absurd,because their stated basis for this is to reinstate my driving privileges in Delaware,of which I care nothing about."
Under the DLC if you are suspended in DE then you are suspended everywhere that participates. $145 is cheap. Pay it and see if they will let you attend an approved class in OH and send in the paperwork. Getting stopped and charged with driving on a suspended license will be far worse.
"That's just my opinion, then again I might be wrong." Dennis Miller