If your numbers are at or above the averages for OSU, you should apply if interested. If you search past SDN threads, you'll see that lots of oos applicants without super stellar stats have been admitted, and my hunch is that OSU wants to matriculate as many OOS students as the legislature allows because the oos people pay more tuition, raise average scores and bring in some diversity. I know this is true at my school anyway.
The other good thing about being an oos applicant to OSU is that they heavily cull the oos applicants before interviews, so if given an interview, you know your odds are as good as instate students. If you're curious about this, check out the USNews data, paying particular attention to the number of OOS students interviewed who are accepted. So really all you have to lose when applying as an oos applicant is the application fee. If they give you an interview as an oos person, they're pretty interested in you.
As for UMDNJ, unless things have changed, they give pretty much no preference instate applicants. The thing is that all their students can gain NJ residency very easily, so their numbers make it look like everyone is instate, when lots of those people weren't until they started school there. My understanding is that OUCOM doesn't show much Ohio preference, either, but they do require oos students to sign a 5-year contract promising to practice in Ohio.