I heard my coworkers received subpoenas from the lawyer in our company.
You
heard this? What exactly does that mean? Did any individual show you a subpoena that he/she had received? If so, that should give you a lot of information. Also, a subpoena is an order from the court (which can be issued by an attorney for a party to a pending action or by the court) that directs someone to give testimony and/or produce documents. It would make no sense for your employer's in-house attorney (presumably what you mean by "the lawyer in our company") to serve a subpoena on any fellow employee.
Is it possible this person who said they want to sue me contacted my work and wants testimonies from my coworkers?
Sure. Just about anything is
possible.
maybe I should contact the lawyer at work who apparently sent those notices to my coworkers?
So...now its "notices," not subpoenas? Whether you contact your employer's in-house attorney is obviously up to you.
Is it possible the person suing me is recklessly asking for subpoenas to my coworkers without having a case, just as in discovery period before they file a lawsuit ?
This doesn't even make sense.
Is this even legal to contact somebody's coworkers who are irrelevant?
There are no laws that preclude a person from contacting any other person, and "relevancy" is a concept that only exists in legal proceedings, and disputes over relevancy are resolved by the judge.
You used words like typically and generally, do it means that or could happen otherwise?
There are no circumstances in which a subpoena relating to a civil case can be issued without a case being filed (criminal subpoenas are very different, and I don't have any familiarity with the relevant procedures).
I'm very confused as I'm not 100% sure the subpoenas regard me but should I be notified if they do?
Maybe. Depends on a lot of factors.
At what point should I be contacted by the party that sues me?
"Should"? I don't have great familiarity with the Ohio Rules of Civil Procedure, but plaintiffs are typically required to serve defendants within 60-90 days after filing suit.
Another option is can they sued me as Jon doe and not use my name so I wouldn't know if I ask court?
The only reason for anyone to file a "John Doe" lawsuit is if the plaintiff doesn't know the defendant's true identity. This happens a lot in cases arising out of online context. For example, you might want to sue me, but you don't know who I am because I post under a screen name. Therefore, you could sue "zddoodah" and seek one or more subpoenas to try and discover my true identity. If you can't discover my true identity, then your lawsuit cannot proceed.
Until you ascertain additional information, there is no point in continuing things here any further.