He was descended from the family of Egill Skallagrímsson, the so-called Mýramenn. For most of his life he lived in Norway, with the kings Sigurðr Jórsalafari, Haraldr gilli and the sons of the latter, especially Eysteinn Haraldsson, whose marshall he became. After Eysteinn's death (1157) he composed the poem Elfarvísur for the nobleman Gregorius Dagsson, referring to his victory over Hákon herðibreiðr at Göta älv.
The best known of Einarr's drápur is Geisli ("Ray of Light"), about St. Óláfr Haraldsson. This drápa was recited in the Church of Christ in Nidaros in the presence of the three Norwegian kings of the time, Eysteinn, Sigurðr and Ingi, along with the first Norwegian archbishop, Jón Birgerson. The poem is composed in the dróttkvætt metre and it is the earliest completely preserved drápa with Christian content.