If there is no Will, then you need to determine if your father had any assets in his name alone. If his assets were joint or had a designated beneficiary, then they would pass by operation of law, outside of probate. Otherwise, probate administration would likely be required for you to gain access to the accounts. Depending on the value of the accounts, there might be a small estate proceeding available to you.
Since you do not know where the accounts or what your father's other assets might have been, you might want to obtain copies of his recent tax returns, to try to determine where he was getting income from. You should be able to request copies from the IRS website.
Oregon does in fact have a small estate affidavit option. You could file that, and then inquire of the bank about balances. The bank should give you that information. There are limits on when you can file a small estate affidavit. There are forms you can buy, that include instructions. If the value of the assets is over a certain amount, or if the Banks are not cooperating, then you may have to file a probate.