How long does a judge have to rule on an objection for a law suite in ohio?

How long has it been? Unless there is a statute, court rule or judicial protocol giving a specific period of time, then it is up to the Judge. You can try to politely prod him or her by writing to the Court Clerk asking for the status on the ruling. If it's a really long time, you can file a Writ of Mandamus and then ask the Judge for recusal on all further rulings. You could also file a complaint with the Judicial Conduct (or similarly named) board. Talk to your lawyer about this though, before you do anything.