1) Check first with your local public library! Public librarians know how to find all sorts of genealogical information in print and online and have networks for asking other librarians when the specific question is particularly vexing.
2) In Oregon, public libraries may have these subscription databases that you can search, sometimes remotely:
a) America’s Obituaries and Death Notices
b) Biography and Genealogy Master Index
c) Ancestry Library has an Oregon Death Index. It’s similar to the SSDI except it has Oregon Death Certificate numbers (but no SSNs). Call your library. Some libraries subscribe to it, but not necessarily as a remote access database so you may need to visit your library, use their local email reference service, or use the Oregon statewide one, L-net.
4) For official, certified copies of death certificates, you need to contact your state’s vital records departments. In Oregon, use the Center for Health Statistics.