Can landlords remove appliances that they rented with the apartment before a court ordered eviction in the state of Ohio

There is no law that says they can't. They just can't prevent your occupancy, unless you are willfully damaging the property.

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Most people won't be helpful to someone being evicted without a clear idea why it's happened. Too many either steal the appliances or they deliberately damage the apartment.

I seriously doubt a landlord can make any changes to his contract without due notice to the tenant, or a court order. Much depends on what the contract says. Care to share those details?