Work out of state

Are you a W-2 employee?   If you are a W-2 employee, then, no, you cannot deduct rent as a job-related expense on your federal tax return.

Sorry---W-2 employees cannot deduct job-related expenses on a federal return.  Job-related expenses were eliminated as a federal deduction for W-2 employees by the tax laws that changed for 2018 and beyond.  Your state tax laws might be different in AL, AR, CA, HI, MN, NY or PA.

Q. Can I deduct the rental expense and mileage from my federal and state taxes?

A. No.  Starting in 2018, employees  (W-2 recipients) are no longer able to deduct any job expenses. 

 Even in the "old days", the rent and travel your describe would not have been deductible.  That's a personal decision and not a job requirement. 

Even if you are a contract employee or independent contractor (you get a 1099 instead of a W-2), your expenses would probably not be deductible (it would depend on more details).