[2] Skáldatal reckons Þórðr among the court poets of both Óláfr Haraldsson and Eiríkr Hákonarson.
In Óláfs saga Tryggvasonar en mesta a short story is told of Þórðr.
In the reign of Olaf II, he had travelled to the Holy Land intending to visit Jerusalem.
On the way he meets a mysterious tall man who converses with him in the Norse tongue and tells him to go back since the road ahead isn't safe.
Þórðr does as he is bid and when he brings the stranger's greeting to Hjalti, he is told that the man must have been Olaf Tryggvason, still walking the earth long after his defeat at the Battle of Svolder.