Ohio election laws require statewide minor party candidates in primaries to submit at least 500 signatures to be on their own party’s primary ballot. According to this story, the Ohio Libertarian primary petitions for Secretary of State, Treasurer, and Auditor did not have 500 valid signatures. Also the Green Party’s primary petitions for Governor and Lieutenant Governor also failed to contain at least 500 valid signatures.
The Libertarian primary petitions for Governor-Lieutenant Governor and Attorney General did have at least 500 valid signatures.
These parties could still potentially nominate candidates by write-in votes, but 500 write-ins would be needed. In 2012 the Ohio Libertarian and Green Parties tried very hard to nominate their U.S. Senate candidates by write-ins at the primaries, but did not succeed in getting the needed 500 write-in votes.
It’s also possible that the various excluded candidates can demonstrate that they really did have enough valid signatures. The primary is May 6.