Here are some ideas on how to get cheap bikes:
Site where people sell all sorts of things. They have a lot of bikes. Tunturi, Nopsa and Crescent are especially good names.
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.
Some used bikes here as well.
Cash store sells and buys second hand items. Kastelholmantie 2.
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.