There is a device that can be installed by an animal control service that allows the squirrels to leave but not re-enter. They can also verify all entry points have been sealed as well. I am not sure what the breeding season is for Ohio, but assuming you have southern flying squirrels there then there may be more than one breeding cycle per year anyway (sorry but I am several states away so not the best source of info on your area).

Thanks Midwesterner for the reply.

Yes, they are the southern flying squirrels - I didn't realize they had several cycles per year.

I was hoping to avoid the cost of an exterminator but I might have to go that route.

Unfortunately, an animal control service might be more efficient. You could easily kill the squirrels but then you will still have the entry points open, more will likely move in at some point, and you have dead, skinky squirrels too. The real key is to get those entry points sealed. An animal control service that just removed the squirrels without sealing the point of entry is just wasting your time since the real problem has not been addressed (which is the fact that your house is not properly sealed to keep rodents out).

One other option would be to observe where they are coming in and out of if it's not obvious and seal the spot (and anywhere else that looks feasible) yourself.

There is also a device called a one way exclusion door that let's them out but not back in. You can use this to make sure no adults get sealed in. I put a link to one of the devices here.

Here is a link that might be useful: One way exclusion door