@shayschrode --
Your home state of KY can tax all your income, regardless of where you earn it. Therefore your employer was correct to withhold KY taxes.
KY and OH have tax reciprocity for W2 income. Assuming your income is reported on a W2, see Question #2 on this OH webpage for the procedure to follow to obtain a refund. Your W2 income is not taxable by OH.
https://tax.ohio.gov/help-center/faqs/employer-withholding-refunds/employer-withholding-refunds
If you never actually worked in Nebraska (or as a telecommuter for a NE-based employer), your income is not subject to Nebraska income tax. To obtain a refund, you must file a non-resident NE tax return on which you show the NE withholding but allocate zero income to NE. This should result in a full refund from NE.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
