Superdog! The one on the S. Park Blocks is open on the weekend. My fave is the Zweigle white hot (from the Rochester NY area): http://www.superdogpdx.com/contact.htm
If you have a sandwich at Kenny & Zuke's, you'll get two meals out of it...maybe not cheap, but a good value.
I think Hot Pot City is open on Sunday, though that is at the south edge of downtown. Great time of year for it, though!
I think the Flying Elephants in Fox Tower is open on Sundays (an offshoot of Elephant's deli) - lots of choices under $5 there.
I'm guessing the Rialto is open (do they actually close? ;o)
1438 SW Park Ave, Portland, OR 97201