If your permanent home (your "domicile") is in KY, you have to file a KY tax return no matter what.
Whether or not you also have to file an Ohio tax return depends:
If you spent more than 212 nights in Ohio in 2016, Ohio will consider you a resident for tax purposes, and you'd also have to file an Ohio tax return (in addition to your KY return). http://www.tax.ohio.gov/ohio_individual/individual/residency_status.aspx
If you spent fewer than 212 nights in Ohio, and your income from Ohio consists entirely of W-2 wages, you would be considered a non-resident of Ohio, and you would not have to file an Ohio return. That's because KY and OH have tax reciprocity for W-2 wages. Your wages would be taxable only by KY. (In your case, however, you would have to file an OH return showing zero OH income, in order to receive a refund of the withheld OH taxes.)
If you are a legal non-resident of OH by the definition above, you should submit this form to the Ohio tax authority: http://www.tax.ohio.gov/portals/0/forms/ohio_individual/individual/2016/PIT_ITDA.pdf
Finally, if you never lived in or worked in Illinois, you don't have to file an Illinois tax return. The fact that your employer is located there is irrelevant.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
