Tom Inglesby, Broker
RE/MAX Equity Group
Everyone has given you the right answer and my experience with the city of Portland is very good. They are always easy to reach or call back in a reasonable time, and they are very helpful. Having said that, from what I've "heard" (keep that in mind!) as long as you're not doing any of the piping and using what was there, you probably don't need a permit although it depends on what you're planning.
However, its a great question because I do want to caution you that we have very savvy buyers in 97211 (where I live and work) and they know how to get on portlandonline.com and check for permits. So as you point out, it wasn't permitted when you bought it so it would be good to have them permit all the work to satisfy a potential buyer. It probably will not cost you as much as you might think. Best to you, and please let me know if you don't have a Realtor to help you in NE and I would love to apply for the job!
You will need to contact the permit department with the City of Portland. I don't believe that permit fees are too expensive. In order to properly complete the project downstairs it will need to be permitted and inspected through the city. In my opinion I wouldn't think you'd have to do the whole basement, just the bathroom.
Have a great day,