Some songs from Iceland which have been sung at previous NHMs:

• Þat mælti mín móðir: traditional song whose lyrics are attributed to viking chieftain Egill Skallgrímsson (c. 904 – c. 995) who, according to Chris Foster, was famous for three things: “one was getting drunk, one was killing people, and the other one was being an absolutely brilliant poet.” The song is about sailing and slaughtering people.
  You can find several recordings on Youtube, e.g. here sung by Icelandic children and here by adults, first in a gregorian style and then in organum style.

• Hýr gleður hug minn: traditional Icelandic song from the songbook of Ólafur Jónsson á Söndum (1560-1627). You can find more stanzas of the song here. It was taught at the NHM 2010 in Gjøvik by Bára Grímsdóttir & Chris Foster.

• Ó mín flaskan fríða: Another traditional song from Iceland, this one written by Eggert Ólafsson (1726-1768) and sung in tvísöngur style (parallel fifths with crossing voices). Taught by Bára and Chris at the NHM 2011 in Broby.

• The Völuspá tune was published in 1780 by Jean-Benjamin de La Borde in his Essai sur la Musique Ancienne et Moderne. De La Borde claimed that this was one of the melodies which Icelanders use to sing poems from the Edda. It was taught at the NHM 2008 in Lund by Kåre and Tove Lie and Maja Marcussen. You can listen to Maja’s version on her website here.