Short answers, pulled from the story.
The Gutasaga is a saga about the history of Gotland before its Christianization, including a creation myth, an account of emigration linked to the historical Goths, and a description of how Gotland entered into a relationship with the Swedish kingdom. It was recorded in the 13th century and written in Old Gutnish, a variety of Old Norse.
The sole surviving manuscript of the Gutasaga, the Codex Holm. B 64, is kept at the National Library of Sweden in Stockholm. It dates to around 1350 and is preserved alongside the Gutalag, Gotland's legal code.
Tjelvar, known in Old Gutnish as Þieluar, is the mythological first settler of Gotland. According to the saga, Gotland was under a spell that kept it submerged during the day; Tjelvar broke the spell by lighting a fire on the island. His descendants, through his son Hafþi and daughter-in-law Hwitastierna, became the three founding brothers of the Gutes.
According to the Gutasaga, Hafþi's three sons, Guti, Graipr, and Gunfiaun, each received a third of Gotland, called a þriþiungr. Graipr held the northern third, Gute the middle, and Gunnfjaun the southern. This division remained in Gotland's legal structure until 1747 and persists in the church's organization into three Deaneries.
The Gutasaga describes an emigration in which overpopulation forced every third person off Gotland; these emigrants eventually traveled along the river Dyna through Russia to Greece. This account is associated with the historical migration of the Goths during the Migration Period. Eusebius of Caesarea reported the Goths devastated Greece and surrounding regions in 263, and the Dvina river mentioned in the saga fits the archaeology of the Wielbark culture.
Awair Strabain is named in the Gutasaga as the man who arranged the mutual agreement between Gotland and the king of Sweden. The saga places this event before the end of the 9th century, consistent with a report by Wulfstan of Hedeby that Gotland was subject to the Swedes.
The asteroid 137052 Tjelvar was named after Tjelvar, the mythological founder of Gotland from the Gutasaga. The name was chosen in 2011 through a competition hosted by the Swedish Astronomical Society in Visby.