I don't know about Ohio. Some States have gone overboard like Alabama, Tennessee, Arizona and they have become xenophobic and anti immigrant. In Texas whether your illegal or from Mars you can get a marriage license as long as one party can identify them selves with an ID and there is a 3 day waiting period. I don't know what the State law in Ohio is. Why don't you call your county officials without going there in person and simply ask them if I'm here on an expired visa can you apply for a marriage license. If you get married, you can have your wife sponsor you for a green card as a permanent resident since you are an immediate relative. Good luck.
You need to check the requirements for the issuance of a marriage license in your state/county, which are usually available online.
The information offered is general in nature and not meant to be relied upon as legal advice. Please consult an attorney prior to making legal decisions. Visit us at www.tunitskylaw.com. Contact us at 713.335.5505 or email at firstname.lastname@example.org. Veronica Tunitsky offers in-person, as well as telephone and email consultations.
The local rules may vary from State to State and county to county, however generally, as long as you can prove your identity, getting a marriage license should not be an issue. After you get married, your wife can sponsor you for the residency.
Nothing in this post shall be construed as a legal advice. If you need advice regarding your particular situation, please contact my office directly. This information is transferred without an intent to creat an attorney-client relationship.
From what you have stated, i dont see any reason why you couldnt get a marriage license.
This answer is for general information only and is not intended as legal advice regarding your specific situation. In order to assess your legal matter properly and obtain legal advice, you must contact an attorney directly. Provision of this general information does not create an attorney-client relationship.