If you owned a bar in Oregon and refused service to a drunken customer, could you be sued?

Someone can always sue for something, its whether they win or not. There are actually many laws on the books that prevent people and establishments from serving alcohol to intoxicated people.

You could be sued.

They'd never win the law suit, but that doesn't stop them from filing. The liquor law is pretty clear on the matter, as is civil law, the burden of not serving drunks is entirely on the establishment.

it is easier to sue and win for serving a drunk, than for not serving one.

No, as long as you apply the rules of "drunkenness" impartially (without regard to race, religion, gender, etc.).

Of course, some moron might try to sue you, and he/she might even get into court, but bars have an ironclad defense: they can be held responsible if a drunk from their place hurts or kills somebody.

Its actually your right, and obligation to refuse to serve alcohol to someone who appears intoxicated

No, you could be sued if you did serve him if he hurts himself or anybody else