Eriol (Cottage of Lost Play):

Described as a "traveler from far countries" (HOMEI.13), Eriol is also described as a son of Eärendel.
'Sons of Eärendel' were children who as newborns, had been touched by the light of the star Eärendel.

Not much seems to be known about his background or origins, not even his real name. Eriol acts as the link between the lands of Men and the earlier ways of life when faries and such were able to interact with Men. An example of this is at the end of the Cottage of Lost Play, when he describes a tradition within his family remembering the same tale told by Lindo and Vaire, only from a different perspective.

The name 'Eriol' is not his real name, but instead one which was given to him by the inhabitants of Tol Eressëa. It translates into English as One who dreams alone (HOMEI.14). His real name is not recorded anywhere.

Eriol (Cottage of Lost Play Commentary):

Eriol is said to be from the Danish regions of Northern Europe, ca. the fifth century C.E. Before his journey to Tol Eressëa, Eriol was named Ottor, but called himself Wæfre, which meant 'restless'.

Eärendel (Cottage of Lost Play):

Eärendel was clearly a great journeyer with the ship Wingilot. He sailed searching for the city of Kôr. Nothing is said about his parentage or his life before this voyage.

He has been called the father of those who wander, especially those who wander the seas, such as Eriol.

The Book of Lost Tales One (HoME.I)
The Book of Lost Tales Two (HoME.II)
The Lays of Beleriand (HoME.III)
The Shaping of Middle-Earth (HoME.IV)
The Lost Road and Other Writings (HoME.V)
The Return of the Shadow (HoME.VI)
The Treason of Isengard (HoME.VII)
The War of the Ring (HoME.VIII)
Sauron Defeated (HoME.IX)
Morgoth's Ring (HoME.X)
The War of the Jewels (HoME.XI)
The Peoples of Middle-Earth (HoME.XII)