So, the majority of streams around the Portland area are going to be closed to trout right now. Once you get down closer to Eugene to the south, and over the Cascades to the east, then you can find streams open right now for trout.
There are a few streams open out toward Astoria for catch and release trout fishing but they might be difficult to get to due to private land owners, etc.
At the end of April, there are a few streams that open for trout fishing and then the rest open at the end of May.
What I usually do is just scour the reg book in a certain zone/area and see what I can find. If you woudl like more info, feel free to shoot me a PM and I will see what I can share.
-Spydey