What is the genre of the Ievan Polkka?
The melody the song uses is often found as "The Finnish Polka". It can be classified as "Scandinavian Folk" or "Nordic Folk". The tune itself has also been adopted by some Celtic musicians, so you may find a similar style music in the Celtic Tradition as Celtic Mouth Music.
In this case the tune uses the natural Minor scale. Some of the melodies of both Scandinavian and Celtic traditions use scales other than straight Major and Minor, such as Dorian Mode, which lends a slightly different sound to the melodies.
The Levan Polkka can be classified into several categories.
Firstly, it is a Polka.
Secondly, it can be categorised as a capella.
The problem is that there is not many polkas that are performed a capella, so you'll have a difficult time finding other examples. I will leave it to other answerers to provide other specimens of this uncommon union. But the fact that this polka is performed a capella has made this specific polka both a standard and a classic.