Here are some ideas on how to get cheap bikes:
http://www.tori.fi/uusimaa?q=polkupy%F6r%E4&cg=0&w=1&st=s&ca=18&md=th
Site where people sell all sorts of things. They have a lot of bikes. Tunturi, Nopsa and Crescent are especially good names.
http://www.greenbike.fi/kpyorat.html
Sells fixed and test-driven bikes at 50 €- 500€. 30 days’ guarantee. New bikes brought to the shop are bought quickyl so there isn’t much of a selection, but it’s worth checking out since it’s in the city center. Located at Bulevardi 32. Open everyday at 10-18:00.
http://www.polkupyoraetappi.fi/kirpputori.php?group=k&group1=49
Some used bikes here as well.
http://www.cash-store.info/urheilu_harrastus.html
Cash store sells and buys second hand items. Kastelholmantie 2.
http://www.huuto.net/fi/showlist.php3?status=N&tits=polkupy%F6r%E4&x=0&y=0
An internet bidding site that sells just about anything. Depending on the seller, you may be able to go see the bike before making a decision. Registration is obligatory in order to place bids.
The police sell bikes that have been found/abandoned every year at auctions. The dates can be found here. Unfortunately the information is not available in English, but you can check the date and place.