Ásynjur
Eir
A goddess whom Snorri ranks third among the Ásynjur and calls 'the best physician'; a maiden of the same name sits at Menglöð's knees in Svipdagsmál.
Eir is a goddess known almost entirely from one sentence. In Snorri's list of the Ásynjur, the goddesses of Ásgard, she comes third, after Frigg and Sága: "she is the best physician" Gylfaginning 35. Snorri tells no story about her and gives her no family. In the hosted Brodeur translation the name is printed "Fir", evidently a misprint for Eir.
The name turns up once in the poems. In Svipdagsmál, the giant watchman Fjölsviðr lists the maidens who sit at Menglöð's knees, and the last pair are "Eir and Aurbotha" Svipdagsmál 54. These maidens bring aid to anyone who makes offerings to them and guard people from danger Svipdagsmál 56, which fits a helper or healer. Svipdagsmál is a late poem, preserved only in paper manuscripts, and it does not say that its Eir is Snorri's goddess.
So the evidence is thin: a name meaning "mercy" or "help", one line in Snorri, and a namesake in a late poem.
In the sources
Quoted from the hosted translations; each line is checked against the text when the site is built. Select a reference to read it in context.
The third is Fir: she is the best physician.
Bjort and Bleik, Blith and Frith, Eir and Aurbotha.
Soon aid they all who offerings give On the holy altars high