How can I find a lawyer that is located in Ohio and is licensed in NH?

It is unlikely that you can find one, but also unlikely that you really need one.  You can hire a NH attorney, or, if you have some reason you need an Ohio attorney, that attorney can probably be admitted to practice in NH for purposes of this one case (pro hac vice), although this may require that you pay for local counsel as well, who would do much less of the work.