The answer will depend upon what your home of record is.
Assuming you were residing in Ohio when you joined the service, you will file your Ohio return as usual.
However, since you are stationed outside of Ohio, you can also deduct any active duty military pay on Ohio Schedule A.
Essentially, you will not be liable for any income taxes on your military pay and allowances while you are stationed outside of Ohio.
See the following for more information on the credits you are entitled to.
Ohio military taxation
Since you are now in Tennessee and as Tennessee does not impose any income taxes, you do not have any filing requirements for the income you earned while stationed in Tennessee.
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