He is perhaps best known as the Allsherjargothi (supreme head) of the official Icelandic Àsatruarsofnudur (or Àsatru-sect), devoted to the survival of the heathen religion of pre-christian Iceland. Amongst others things, Sveinbjorn got Àsatruarsofnuthurinn officially recognised as a religious body in 1972 after a long battle with the Ministry of Justice & Ecclesiastical Affairs—the first non-Christian group to receive such rights. He served as the Allsherjargothi from the start.

Apart from the farming the main bulk of Sveinbjorn's work lay in the Rimur and other poetry with the older Germanic form and metre.

Rimur is a kind of "sung Poetry" and is closely related to the epic singing traditions of early Europe. Rimur singing is similar to vocal chanting from the Middle East, but the forms are not related and unlike the Arabic counterpart the "sung poetry" of Iceland has no tonal scale but is a free-form wave of sound. It's a strict form of expression with stability in the volume, pitch, tempo and length of syllables.

Using Rimur singing as a basis Sveinbjorn almost single-handed re-created the art of epic singing used by Scandinavian poets of pre-Christian times, who created such masterpieces as Voluspa and Beowulf (Bjolfskvitda).

As the Nordic intelligentsia had dismissed his singing as "the primitive groans of farmers", Sveinbjorn turned to a younger generation of listeners with his offerings. In the late seventies and early eighties he performed with new wave, industrial and punk artists like Psychic TV, Theyr (members later in Psychic TV, Killing Joke, Kukl, Sugarcubes & Frostbite) and Purkur Pilnikk (whose members later started Kukl & the Sugarcubes)—earning him the respect and admiration of younger music fans and the disrespect, hatred even, of self-appointed "cultural moguls" and poetry/literature scholars. His records where published by independent rock labels, rather than the expected classical or early music specialist labels.

Sveinbjorn's vocalization of the lays of the Elder Edda (Eddu Kvaedi) are available from the English record company "D.U.R.T.R.O." (United Dairies) as "Current 93 Presents Sveinbjorn Beinteinsson : The Eddas".