You and your fiancee need to go to the courthouse downtown (the old building not the new one). Go to, I believe, the 22nd floor to get a marriage license. Your fiancee is 18 so she does NOT need her parents' consent as she's an adult. Her legal status in the US is irrelevant for Ohio marriage license purposes. You both need IDs; your fiancee should bring her passport. And it costs $50.
After you're married, you may be able to help your fiancee with her legal status in the US (depending on many factors that I'd be more than happy to discuss with both of you once everything is done). Good luck and Congratulations.
This information is intended as general information only. This communication does not establish an attorney-client relationship between me and the asker.
I agree with Ms. Hamayel, who has the immigration expertise I do not have. I was not sure what effect citizenship would have on the right to marry. One correction, you will want to go to the 23rd floor of 373 S. High to obtain your marriage license.