What is Ohio Guard militia?

Answer 1

Ohio Guard may be a shortened form of Ohio National Guard. Under the Militia Act of 1903, the National Guard is identified as the organised militia, and are considered as such during periods of non-activation and state activation, but become federal soldiers when activated at the federal level.

It may also be an informal name for Ohio's State Guard force, properly known as the Ohio Military Reserve. A State Guard force is an indigenous militia raised by a state governor, and which are not under the federal web which the National Guard is under. These units typically serve as auxiliaries to the National Guard, and are often oriented more towards CERT and disaster response than they are towards actual military/paramilitary activity. Not all states have raised such forces, and not all forces calling themselves "State Guards", "State Defence Forces", etc. are organised as legitimate State Guard Forces under the governor. See the related Wikipedia link at the bottom for more information on State Guard Forces.

While I've found a number of private militias which exist in Ohio (at least on paper), I'm unable to find any reference to any such organisation calling itself the Ohio Guard.