Yes, you can bring your Glock. Theoretically you can keep it on campus, although UofO seems to think they are somehow exempt from the same laws that everyone else has to obey and (illegally) ban guns on campus -- you probably don't want to be the one to have to pay to drag them through the courts, so it would be wise to keep it off campus.
Residency is one of those "fluid" things.
If you do a few things to make a gesture that you intend to reside in Oregon, then you are resident.
The most obvious things to do might be looking into swapping you CA driver's license for an OR one, and if you bring up a car, think about registering it in OR .. I don't know how long/expensive the registration process is, but my guess is that you would still end up better off -- the tags are $30 for 2 years here. Of course if you want to ever take it permanently back to CA you would have to re-register it there, which might not be cheap.
Once "resident" you just walk into a gun shop and hand over money and ID (driver's license), fill out the ATF forms, wait for the instant check call to go through, and walk out with your lower.
Alternatively, you can skip the residence part and just do a private purchase of the lower. There is certainly someone on this boeard who might have what you want.