You report all of your income on an Oregon state tax return, regardless of the source of the income when you are an Oregon resident.

If your WA employer is not withholding OR state income taxes you need to be paying OR estimated taxes during the year so you will not be hit with penalties for failing to pay state taxes.

Since you're a resident of OR, you will pay OR state tax on the income you earn, regardless of where its earned.

How would I know if my WA employer is withholding OR state income taxes and also how would I go about paying estimated OR taxes? 

Look in boxes 15-17 of your W2 to see if Oregon Taxes were withheld. To make estimated tax payments, there is section in your oregon state return that mentions A few things before we wrap up your state taxes.  Go to other forms>estimated taxes for next year. Here is what this section looks like.

@Hmontoya 

If you prefer, you can make your Oregon estimated tax payments online here:

https://revenueonline.dor.oregon.gov/tap/_/