The Ásatrúarfélagið ("Fellowship of Æsir faith"), which he founded in 1972, and for which he acted as goði (priest), was officially recognised as a religious body in 1973. Sveinbjörn lived his entire life in West Iceland. From 1944 on, he was a sheep farmer while also pursuing literary interests on the side.
He published a book of rímur in 1945, a textbook on the verse forms of rímur in 1953, two volumes of his own verse in 1957 and 1976, and edited several anthologies. Sveinbjörn is regarded with much respect and affection amongst Ásatrú. Not only was he a well known rímur singer, or kvæðamaður, in Iceland, he also gained an audience and followers in Europe and North America.
He sometimes performed at rock concerts and is the opening act in the film Rokk í Reykjavík, directed by Friðrik Þór Friðriksson. Sveinbjörn can be heard singing on the bootleg album "Ragnarok (A New Beginning)" by Burzum, on the last track of the album entitled "Havamal". Sveinbjörn can be heard performing Ásatrú marriage rites for Genesis and Paula P-Orridge (now Alaura O'Dell) on Psychic TV's LP Live in Reykjavik and on the double LP entitled Those who do not.
In 1982 Sveinbjörn released an album, Eddukvæði (Songs from The Poetic Edda), in which he recites in rímur style 75 stanzas from Hávamál, Völuspá and Sigrdrífumál. The album, on the Gramm label, included a booklet of the poems in Icelandic, with translations into English, Swedish, and German. Additionally, former Psychic TV member David Tibet (né David Michael Bunting) released a CD of Sveinbjörn performing his own rímur and reciting the traditional Poetic Edda under the title Current 93 presents Sveinbjörn 'Edda' in two editions through the now defunct record company World Serpent Distribution.