Most states have durational residency requirements for divorce -- you must live in the jurisdiction for a continuous period of time before you can file there. Washington law does not include such a rule, but it does impose a waiting period before the court will actually grant you a divorce.
Residency in the State
You must be a resident of Washington in order to file for divorce there, but not for any statutory period of time. If you live in Oregon, you can't just drive over the state line and file, but you can rent an apartment with the intention of living in Washington and file for divorce the same day you arrive.
Effect on Service
If your spouse doesn't live in Oregon, this might prolong the divorce process a little. Normally, he would have 20 days to respond to your papers after you officially serve him with a copy. If he lives out of state, however, this time limit can extend to 60 days.
Although you don't have to live in Washington for a required period of time before you can file, the state has a waiting period. The court can't grant your divorce until 90 days have passed from the date your spouse is served with your divorce petition. If you haven't resolved issues of property, debts, custody and support by this time, your divorce could take longer – you must address all these issues before the court will issue a divorce decree.