Your best bet might be to call the Department of Revenue at one of the phone numbers under the Personal Income Tax dropdown on its Contact Us page.
It sounds like your Oregon tax return is being rejected after you've electronically filed your state return. I believe you're suggesting that Oregon's eFile system is rejecting the return because you have an ITIN.
However, Oregon may allow Earned Income Credit even when ITINs are being used. This is why I suggest you contact the revenue office -- the use of an ITIN, in and of itself, wouldn't seem to be a disqualifying factor.
According to Oregon EIC for ITIN filers in the Publication OR-17:
You may be able to claim Oregon’s EIC for ITIN filers if you would have qualified for the federal EITC this year but couldn’t claim some or all of the credit only because you, your spouse, or qualifying child(ren) don’t have an SSN that is valid for work. If you don’t qualify for the federal EITC for any other reason, you can’t claim Oregon’s EIC for ITIN filers.
There's a particular numeric format that identifies a number as an ITIN -- see the IRS' Publication 4757, Individual Taxpayer Identification Number (ITIN).
