TL; DR: It may be possible to do but you have to be really careful and even then you can't ensure that the police won't attempt to charge him. In addition, since he is helping you out and you are staying at his place, you should take his wishes into consideration. It may be best to wait until the situation changes.
No one is saying that you can't buy a gun and that you lose your right to self-defense, but they are saying that under the current circumstances, it may not be the best ideal.
I don't know Ohio laws or case law, so take everything that I say with a grain of salt. In no way am I providing legal advice.
There is a doctrine called constructive possession that essentially states that if something is in a person's area of control or where they have access, they are deemed to possess that item. Thus, if you have a gun in the house and it is accessible to the felon, even if it is not his, then he can be deemed to have constructive possession of the firearm.
In some states, it is possible to have a firearm in a residence where there is a convicted felon. However, in these instances, it is imperative that the firearm be kept completely separate from the felon. This would generally be a safe that he does not have the combination to and has no access to. However, this is not an ideal course of action for several reasons. 1) As a term of their felony convictions, sometimes felons have waived the protection against unreasonable searches and seizures and thus the police can search the house at any time for any reason if this is the case. 2) Even if the firearm is kept in a locked safe, this does not mean that the police will not attempt to seize the firearm and charge your roommate with possession of a firearm as a convicted felon. He may ultimately be able to beat the charge in court but it will be a long, expensive fight for him and could put him in jeopardy. You would also likely have to get involved because I would imagine that you would have to be a witness to testify about whether he had access to it. 3) In the event that the firearm is seized and your roommate gets off of any charges, you would still have to fight with the police over the return of the gun and possibly have to get court involvement to have it turned back over to you. 4) You would have to make sure that you don't leave any gun stuff laying around. This means no loose round of ammunition laying out because it didn't fit in the magazine. It means that if you have a range bag that there is nothing left in there. I don't know if there is anything associated with magazines but you shouldn't leave those laying around as well. Theoretically, you really shouldn't even load magazines or clean guns in the home because it would be unsecured at those times. Any of these items are a possible basis for a felon in possession charge for him.
This is not an idea solution, but if you have a car that he does not use, get a car mounted lockbox/safe and keep the firearm in there. The same caveats apply for bringing stuff into the home, but at least it is a separate location. There are additional risks with leaving it secured in the car and you have to be careful of theft, but it would potentially be an option. Alternatively, if you have a friend that can store the gun for you, you could do that. I know that those solutions don't really address self-defense in the home but it would allow you to use a range.
Another important consideration is your friend himself. It sounds like he is helping you out a great deal and providing you essentially with a means of getting by. Even if his felony conviction doesn't disqualify you from owning a gun, you really should consider whether you want to put him at risk of future charges and put his freedom in jeopardy. In addition, since he is helping you so much and it is his name on the lease, I believe that you should respect his wishes. If I were in his shoes and found out that you had brought a gun into the house without my permission and knowing that it would potentially put me in jeopardy, you would be gone because I would not be willing to take that chance. You have to be careful to make sure that this will not happen to you, even if you figure out a way to possibly protect him from any charges. If you don't have anywhere else to go or a means to get your own place, it may be best to wait.