I agree with Josh, this is not an easy situation to be in. The current vacancy rate in Portland is really low, so the landlords can afford to be really picky. Letters of explanation will help, depending on your situation, perhaps renting a room rather than an entire apartment would be the best way to build back up your payment history and credit.
Sorry to hear about your situation but the landlord you are looking for likely has a van down by the river for you. I would suggest concentrating on letters of explanation to your circumstance and full disclosure to any property manager/ owner you encounter. Expect to pay a higher deposit when you find the owner that is willing to rent based on the situation. Not impossible, not easy at all. Good luck!