Am I required to file an Oregon tax return?

you probably have to look at their forms and see what your personal exemption and standard deduction amount to
if your income doesn't exceed it more than likely you don't have to file the state as you don't a federal

Not necessarily. I'm not sure about Oregon tax law, but for the state of PA they require you to file as long as you have earned income of $30 or more ($30 x 3.07%= $1 tax due). I'd check with a local tax professional