I never tried listening to state Department of Corrections (DOC). If they are anything like the sheriff though (Multnomah County SO), their corrections comms are likely super boring. Unless that is someone's special interest or something...
The only prison I know of in Multnomah county is the Columbia River Correctional Institution (CRCI) which is run by DOC, out by PDX airport. Everything else is county jails run by MCSO. If you are monitoring from the Hawthorne area I doubt that you could even pick up CRCI from where you are. I'd suspect you would need to be closer to get their repeater.
You might be able to pick up MCDC (the downtown Portland jail) from where you are, but like I said, those TG's are pretty slow and mundane, at least to me. Even my ex-neighbor's obsession with monitoring fast food drive up windows was more interesting than corrections comms...
We've since moved so I don't have any freqs or talkgroups anymore, but I suspect the info is on the web someplace. Or on this site, in the RR Database.