As a subcontractor not living in the state I worked in, without a contract directly with the homeowner and no written contract with the contractor can I file a lien on the homeowners property
A written contract is not a requirement to securing mechanic's lien rights in Ohio, so your (presumably) oral contract would suffice, as long as you could show with reasonable certainty what amount is owed to you.
For home construction projects such as this one, two additional factors could impact your mechanic's lien rights. First, if the homeowner recorded a notice of commencement prior to starting work on the project, you would then be required to serve a notice of furnishing to the owner in order to keep your mechanic's lien rights. If a notice of commencement was recorded, but no notice of furnishing was served, you likely do not have any mechanic's lien rights.
Second, in Ohio homeowners have a complete defense to a mechanic's lien if the homeowner has paid the general contractor (original contractor) in full for work performed by the general contractor's subcontractors and suppliers (such as yourself).
Both the notice of commencement and the payment are defenses the homeowner may have to any mechanic's lien you file. Aside from those reasons, you most likely have mechanic's lien rights so long as you are within the timeframe (60 days from the last date of work).