JimDandy. If you move from OR to WA you owe nothing on anything you legally own, including your automobile (if you have owned it over 6 months). Just because you move from OR to WA does not mean you have any specific duty to "transfer" your firearms.
They do have a little "got ya" in that if you have owned something expensive that is registerd (like an automobile) for less than 6 months, they assume you purchased it to avoid the sales tax and will try hit you will it anyway. Ya, been there, gone through that,
There is no firearms registration in either OR or WA....so no transfer needed.