It sounds like you may never come across the information you are looking for on the web, short of driving past each station to see what is parked there. And excluding Engine and Truck companies---water tenders, brush rigs, rescues and other special equipment can seasonaly be moved from station to station, that may also explain why the information isn't readily available.
Reference to 300#'d companies as volunteers.......... I would assume the same, as the Skyline Volunteers are Engine 363.
The TVF&R link that Amusement posted should answer a lot of your questions in a round-abouts way. The description of each station describes what Engine (or Truck company) is housed there, however the pictures show two engines stationed there. My guess is that the 2nd (older) engine is a reserve rig, probably designated as (example) E60 as well but only put into service when the primary rig is out of service.
Portland designates their reserve rigs as E14R, T4R, etc., but those numbers are more or less clerical things, you'll never hear them on the radio using those numbers.