You cannot serve your ex in California with an Oregon contempt order. What you can do is have your support judgment registered in California and proceed with enforcement remedies under California law. You would be able to serve him with the contempt if he ever does come to Oregon again.
I don't practice in Oregon but it seems to me that this is a service issue. Service is different than enforceablity. You will follow in the state where your orders are. Service occurs where he is. As long as he lived where the orders are, the court will likely have jurisdiction. If so, then you can serve him via process server or another acceptable means under Oregon law. You should consult a local lawyer to ensure you do that correctly.
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