Generally, say if I have out of state plates and insurance, should the state where I'm currently residing issue me inspection stickers without any problems?

 

no.

In Washington if you are living here more than 30 days you have to change your drivers license and relicense your car.

 

Most states require before you can register you have to have it inspected. Here in TX they will give you a form the inspector fills out that you take with you to the tax office to pay for registration. If you've been in state more than 30 days you are subject to a ticket if caught. How do they know? If you are enrolled in school is the easiest way.

 

that was because of all the people who used to license their cars in oregon to get cheaper tabs, right?

 

Any links with definite info, folks? I find this hard to believe, as about 75% of the cars I see on the lots would be in violation, not to mention that I doubt anyone with west coast plates drives cross-country to get inspected

 

I would say that if you are going to be in an area long enough that you have to get inspected you can count on not only having to do the emissions program for that state, but also have to register the vehicle in that state as well as notify your insurance company of the change.
The state you are in wants money for their roads and want to make sure you aren't polluting their air.
Since the actuary freakers for the insurance companies like to charge specific rates for specific areas I wouldn't be the least surprised to find a clause somewhere in your insurance agreement stating that if you don't notify them of changes in residence that cover a specific period of time that you may be in breach. It would suck bigtime to get into an accident or fender bender only to have some insurance tight a$$ disallow the claim.
My suggestion would be to go on the net and search the motor vehicle department links. Something like this for a start maybe http://www.dmv.org/