Hi,
Welcome to FlyerTalk!
OK, a couple of poins.
You have some Avios and want to get from San Diego to Oslo.
You wish to minimise your fees and taxes, and think (correctly!) that IB charges less tax and fees than BA.
IB, however, has a fairly restricted route network - many flights will actually be BA codeshares. They may, still, be cheaper to book through IB. But they will be towards the BA levels for taxes and fees.
This would apply for MAD-Oslo, since IB do not fly this route, but send you to London to pick up a BA flight to Oslo!
Looking at skyscanner.net it also appears that the "IB" from San Diego to Madrid goes through Chicago or London, so is an AA or BA codeshare!
Have you thought of Air Berlin - they are a One World partner, you can book through BA - and possibly IB - and they fly LA - Berlin - Oslo.
Very low taxes, an only one connection from LA - so you would need to add-on the San Diego leg. AB business class comes recommended.