Yes, Oregon has a right to administer drugs for physician-assisted suicide, because it is part of their law. There is nothing in the constitution that says there is no right do die. In fact, some say that there is a constitutional right to die. Since there is no conflict, Oregon is free to make their own law.
Yes, Oregon does have the legal right to administer drugs for the purposes of physician-assisted suicide. The patient must be sound of mind when making the request and have a terminal illness. In 2006, the Supreme Court ruled that the Attorney General could not charge doctors with a crime in Oregon who prescribed drugs for the purposes of physician assisted suicide.