I did my internship with MetroWest and one of my EMT friends works for AMR. I have not worked/lived in Portland for 3 years now.
http://metrowest.fm/ I worked in the area for years.
AMR Clackamas and Portland have been on external hiring freeze for medics(not sure about EMT's) for years last I checked. AMR also operates out of Clark County. That info maybe out of date now but that is how it use to be. A lady named Jennifer Stoner at AMR who was in charge of recruiting in and around Portland. Ill pm you the last known email i had for her. I herd she got married so I am not sure if her email is the same anymore. If in doubt call AMR Portland
I also worked for a very small agency no one knows about called "Metro" they hire EMT's and medics to do event stand by at the convention center, expo center, and a few other government places. Its actually a government agency that found it was cheaper to have its own guys rather than pay for a contract with AMR or Metro West.
http://www.oregonmetro.gov/
We use to have an agency called Noble Ambulance but they went out of business a few years back.
There is also an IFT/wheel chair company called "Community Ambulance" I have herd nothing but bad things about but it maybe worth checking out. They only do BLS IFT non emergency.
http://www.dexknows.com/business_profiles/community_ambulance-b284478?mkt=62901
aside from those places in the greater Portland area there are no other providers I am aware of besides Fire departments who do not transport except for rural volunteer agencies further out such as these guys.
http://www.molallafire.org/ Further north I hear
North country has a station further north near Clark county
http://www.northcountryems.org/
but for IFT's inside Portland, its community ambulance, metro west, and sometimes AMR