One possible place to catch salmon which is also fairly close to Oulu, is the Kemijoki delta area. I tried a few years ago but never caught one. On the other hand my fishing gear mightn't be strong enough for 10+ kg fish and I didn't have a boat to use, so it's not a big surprise.
I saw a few salmons leaping anyway and talked to a few fishermen who had caught them, so they exist.

The fishing licence costs something like 15 e/day and 50 e/fishing season if I remember correctly and the prices haven't gone up.
In Oulujoki (delta area) you can catch some, too. No idea about how common it is but it's possible!
The most legendary place in Finland to catch salmon is Tenojoki from which I don't have any experience at all.