PSOE : Pre-Security Of Employment
Outside of the University of California system, the term PSOE doesn't have much meaning. Essentially, it's the designation used for Lecturers (i.e., teaching faculty) who are members of the Academic Senate and on track for "Lecturer tenure", which is called SOE, or "Security Of Employment".
There is a roughly parallel track between teaching faculty and research faculty: lecturers PSOE are at the same level as assistant (research) faculty, in that they're both pre-tenure. Lecturers SOE are at the same level as associate (research) faculty, in that they're both post-tenure.