Irish music is of increasing popularity in finland. I think the people of Ireland and Finland are very much alike in many ways. Also the Finnish-Irish Society is a lively organization with members counted by the hundreds. It's the only city where you can find regular gigs. In other bigger towns, like Turku and Tampere, there is occasionally a chance to see Irish music live, but you'll have to be lucky enough to actually find it.
Local newspapers are a good source of information.
In Helsinki there are, at the moment, three places that offer Iirish live entertainment every week. A new Irish bar, called Parnell's, provides live acoustic music on saturdays. The first two places are usually crowded and unfortunately people usually don't pay much attention to the music itself. If you want to go and listen to it, you'd better get as close to the stage as possible. The Finnish-Irish Society organizes an Irish Festival every September.