Tried posting this on UKClimbing Eddie, but it wouldn't work for some odd reason but as you are here now...
I think Oulu is probably one of the less good places in Finland for climbing, as no real rock that close - could be wrong if there are locals watching the might give you more specific info.
There is definitely stuff near Rovaniemi which isn't too far away from Oulu (relatively speaking) and across around Kuusamo, but I haven't heard many stories about it being particularly good. In winter the best iceclimbing in the country is not too far away - a place called Korouma, again not far from Kuusamo. There is a topo guide to the whole country you can buy, but there isn't too much in the north in it.
Keep an eye on Sloppi.net hopefully they will have more info soon for northern Finland. The guys who do it are doing an excellent job, but they are quite sport climbing and bouldering oriented - so just because trad doesn't get too much of a mention doesn't mean its not there or its no good! There is some limited info at http://www.tky.hut.fi/~teepakki/climb/
There is a link there to mountainshop.fi which has some very limited info on Oulu but its all in Finnish.
There is an 'international climbing club' in Oulu which sounds fun I'd start there: http://www.danielides.de/rocknrope/home.html
Expect to learn to ice climb if you are staying over the winter otherwise you'll be condemned to the wall for 6 or more months!
If you are coming down to Helsinki, drop me a line. I can show you around 'our' crags. Try and get to Olhava - its the dogs danglies but a long way from Oulu.