Please help me find the cheapest airline R/T prices from (any city) in
Cebu -or- Manila Philippines to Seattle, WA -or- LAX -or- SFO -or-
Sitka, Alaska (sitka is the final destination but I will consider
airfares finishing in any other majoy US city on the West Coast.)

What I need is an airfare website or a classified ad listing that
deals with international airfares leaving FROM a city OUTSIDE the US.
(not leaving from the US!)

I can't say I have the best answer -- but, I suggest you try one or
both of the following:
1. Speak to a travel agent -- they will likely have access to better
fares, and more airlines than you might have considered. If you are
working in an office, ask who their travel agent is -- those resources
are probably used to finding flights and fares to all corners of the
world.

2. Search airlines that serve that area primarily -- or better, find
out what the country's major airline is and try them:
http://www.philippineair.com/ & http://www.cebupacificair.com/ and try
Quantas (Australian airline) and Air New Zealand.

It's unlikely you'll get a dirt cheap flight... but get to know that
airlines that regularly service the route, sign up for their
newesletters, and if you have time, wait to see what kind of
promotions they run.

Best of luck!