I am an attorney in Ohio.
Yes, it is a felony to possess a centerfire semi-auto with a capacity of "more than" 31 rounds. An AK, for example, is legal with a 30 round magazine since it has a total capacity of 31 (30 in the magazine and one in the chamber). A semi-auto Uzi has a capacity of 33 with the 32 round magazine and is therefore illegal. It is the capacity that is the problem, not how many rounds you put in the magazine. Ohio considers such guns to be "automatic firearms" which is a poor choice of words. Ohio exempts NFA registered firearms so the capacity limit won't apply to your registered subgun.
Having said that, this is one of the most frequently violated and infrequently enforced laws ever. It is not illegal to sell or possess magazines having a capacity of more than 30 rounds in Ohio. I'm going to a gun show this afternoon and I'm sure I'll see plenty of AK drums, forty round mags for various guns etc. I also see them at ranges quite frequently. I used to volunteer to total strangers that I would see with AK's with drums and the like that they were in violation, but after a few rude responses decided WTF, it's their problem if they get caught. The only time I remember people being prosecuted under this section was as an additional count with some other felony i.e. bad guys.
Bottom line, if you have a semi-auto Uzi in Ohio, to be safe stick with the 25 round magazines.
I followed the link to the AR15 website about the case now pending in Toledo and reviewed the court docket on the internet. Unfortunately, the internet access does not permit the viewing of pleadings actually filed. Supposedly, the defendant in that case possessed a registered SBR but is being prosecuted for the over 31 shot capacity. If that it is true, one wonders why he didn't come under the NFA registered firearm exemption. There is some sort of Motion to Dismiss pending and set for briefing this month.
It's possible that the prosecution is taking a very technical approach under Ohio law. The prohibition is against possession of "dangerous ordnance" and dangerous ordnance can include, among others, a "sawed-off firearm" or an "automatic firearm" and , as already discussed, a centerfire semi-auto with a capacity of more than 31 is an "automatic firearm" under Ohio law. I suppose that the prosecutor could argue that an NFA firearm registered as an SBR would not be illegal as a sawed-off firearm, but since it is not registered as an automatic weapon it is still limited to the 31 round maximum capacity. Of course, the Catch 22 is that since the feds have no magazine capacity requirement, one cannot register a semi-auto on that basis.