Credit for Tax paid to another State

It appears there was not a period of double taxation so there will not be a credit for taxes paid to another state.  The credit for taxes paid to another state is designed to mitigate double taxation which comes into play when a taxpayer is double taxed on income earned in a non-resident state by the resident state.  

Typically, a resident state, which taxes income no matter where it is earned, offers that credit when, while living in that resident state a taxpayer made money in another state which also taxes the income. 

It appears in your scenario you were part-year resident in OH and OR and were taxed by those states while you were resident in each state; no double taxation.  Your W2 is showing the taxes withheld for each state according to your residence period as determined by your employer. 

Enter the form W2 state lines as indicated on your form.  Those state line box 16 amounts will be used to allocate the income to each state in state interviews and report the taxes already paid to each state according to the box 17 amounts.