You should have filed a 2017 NJ non-resident return and paid tax only on your wage income for Jan-May. Ohio will give you a credit, or partial credit for what you paid NJ.
Ohio has a reciprocal agreement, on wages, with all neighboring states. No state taxes are withheld or due and you do not normally need to file a return for MI. But OH will tax you on all your other state income.
If MI taxes are mistakenly withheld, you then have to file a MI non-resident return, to get a refund. OH will not give you a credit. You should ask your employer to stop withholding so you don't have to file a MI return every year.
OH is also reciprocal with DC. DC tax should not have been withheld, but that DC income is taxed by your resident state (OH).
