From Section 4117.15, found here: http://www.legislature.state.oh.us/B..._SB_5_EN_N.pdf
(A) No public employee or employee organization shall engage in a
strike, and no public employee or employee organization shall cause,
instigate, encourage, or condone a strike. Whenever a strike occurs, the
public employer may seek an injunction against the strike in the court of common pleas of the county in which the strike is located.
(B) Any person who violates division (A) of this section may be subject
to removal or other disciplinary action provided by law for misconduct. The
public employer, the state employment relations board, or any court of
competent jurisdiction shall not waive the penalties or fines provided in this
section as part of the settlement of an illegal strike.
(C) A public employee who is absent from work without permission or
who abstains wholly or in part from the full performance of the employee's
duties in the employee's normal manner without permission, on the date
when a strike occurs, shall be presumed to have engaged in the strike on that
So far that's all I've found. It does appear that they're actually making strikes illegal for public workers, but I have yet to find what the actual punishments are. I can't tell if there are criminal punishments, or if it's just saying they'll fire you. I'll keep looking, but it's very hard to specifically find what you're looking for in these things, even WITH Ctrl+F.
Several papers have reported that punishment includes fines, and at one point jail time, but that the jail time was removed.