Vali (pronounced like the English word “valley”; from the old Norse Váli) is a Nordic god, whom we only know from a few scattered, temporary references in the old Norse literature. He is the son of the god Odin and the giantess Rindr.  When the god Baldur was killed, Vali avenged his death by killing Baldur’s hunter, another obscure divine figure named Hodr (Höðr).
Valli did this feat when he was only one day old, and Valli may have been born specifically for this purpose, although the sources on this point are not clear. The only other mention of Valli, other than his role in revenge for Baldur’s death, comes from a poem that lists him among the younger generation of gods who survive Ragnarok, the demise of the cosmos. (In some reports about Ragnarok, that is, in other reports, the universe just ends and no one survives.) This lack of other episodes from Vali’s life could support the idea that he was born only to kill Hodr, but it could simply due to the fragmentation of the sources themselves.
The meaning and etymological origin of Valli’s name are unknown. The most convincing theory that has been put forward so far is that the name is derived from the proto-Germanic word * waihalaR “The Arguing One”, which means disputation and ultimately struggle. Valli Goddess
He may or may not have been actively revered by the Northerners and / or other Germanic peoples (in contrast to a purely literary figure). In Norway there is a place called Valaskioll, which comes from the old Nordic Valaskjálf, “Valli’s Crag / Seat”. This could indicate that the area was a place where Valli was worshiped. But the name Valaskjálf is used elsewhere in a more general sense to indicate a place of residence of the divine, so this place name could also refer to a more general religious center or could simply have been used to express a wish on the part of those who called it to live in close proximity to the gods. The meaning of this name, like most of Valli’s personality, deeds and role in Nordic mythology, will remain a mystery to us forever. Valli Goddess
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References:  The poetic Edda. Baldr’s Draumar, stanza 11.  The poetic Edda. Hyndluljóð, verse 29. The poetic Edda. Völuspá, verse 23.  Turville-Petre, E.O.G. 1964. Myth and Religion of the North: The Religion of Ancient Scandinavia. p. 139-140.  The poetic Edda. Vafþrúðnismál, stanza 51.  Simek, Rudolf. 1993. Dictionary of Northern Mythology. Translated by Angela Hall. p. 348.  Ibid.
Longstanding transcription error
Váli is often incorrectly referred to as Loki’s son, although this is most likely an early transcription error. The mistake results from a single passage in Gylfaginning that contained the sentence “Then Loki’s sons Váli and Nari were taken”. Gylfaginning, however, describes Váli as the son of Odin in two other cases. All other documents from this period refer to Váli only as Odin’s son, with the exception of recent copies of the original incorrect text. Valli Goddess
Myths of Valli Goddess
The Váli myth is mentioned in Baldr’s draumar:
Rindr will wear Váli
in western halls;
this son of Óðinn
will kill when one night old –
he won’t wash his hand
still comb head,
before he carries to the stake
– Translation by Ursula Dronke
There was formed from this tribe,
that was slim
a shaft of fear, dangerous:
Hǫðr started shooting.
A brother of Baldr
was born quickly:
he started – Óðinn’s son –
to kill one night old.
And in prose Edda Gylfaginning (where he is described as Loki’s son)
Now Loki was taken without weapons and taken to a certain cave. Then they took three flat stones, put them on the edge and drilled a hole in each stone. Then Loki’s sons Váli and Nari (or Narfi) were taken; The Æsir transformed Váli into the shape of a wolf and tore apart his brother Narfi. And the Æsir took his intestines and tied Loki with them over the three stones: one stands under his shoulders, the second under his loins, the third under his hips; and these bonds were turned into iron.
– Translation by Arthur Gilchrist Brodeur
The prose Edda also mentions him again. Gylfaginning contains this passage:
One is called Ali or Váli, son of Odin and Rindr: he dares to fight and is an extremely happy shooter.
The same text also says that he will survive Ragnarök with his brother Víðarr and the sons of Thor, Móði and Magni.
Ancestry of Valli Goddess
Early mistranslations or confusion led to the only mention of a Váli who is a son of Loki: “Þá váru teknir synir Loka, Váli ok Nari eða Narfi” from the prose Edda, translated as “Then Loki’s sons Váli and Nari were taken” . We find the original of the only reference to Váli as Loki’s son, while even the same text indicates that Baldr’s death was avenged by his brother (in Völuspá 33) and Váli is Odin’s son in Völuspá 51, which is in Baldr’s Draumar is repeated.
In the late period of the Gesta Danorum we also see that Odin is said to have a son with Rinda who will avenge the death of his other son Baldr – although in this case the name of this new son is more Bous than Váli. In all of these stories, Odin immediately goes out – either through seduction, deception or violence – to father this son. [A]
Similarly, if each of these documents attributes Váli to the role of Loki’s son, only in the addendum or translation notes do we see that this transformation was a punishment, although the gift of strength and rage from the wolf was actually known to Odin by warriors is granted ulfhednar, which would make his son Váli a berserk and a possible origin for the ulfhednar legend.
Finally, we see another description in Hauksbók. In this version of Völuspá, verse 34 begins: “Þá kná Vála | vígbǫnd snúa”, usually changed to the nominative Váli to provide a subject for the verb; Ursula Dronke translates it as “Then Váli | battle ties twisted”, which probably refers to Váli, the son of Óðinn, who was conceived to avenge Baldr’s death, and therefore it is likely that he bound Loki, though this is highly unlikely to be a Váli, Loki’s son, who testifies only one line of Edda prose.
Váli (son of Loki)
This article is about a son of Loki in some versions of Nordic mythology. For the son of Odin, see Váli. See Vali for other uses.
In some versions of Nordic mythology, Váli was one of Loki’s unfortunate sons. He is mentioned in the Gylfaginning section of Snorri Sturluson’s prose Edda, chapter 50. After Baldr’s death, the Æsir Loki hunts and captures him. In this version, it’s an unnamed god rather than Váli, the son of Odin, who connects Loki to his son’s bowels:
Now Loki was taken truceless, and was brought with them into a certain cave. Thereupon they took three flat stones, and set them on edge and drilled a hole in each stone. Then were taken Loki’s sons, Váli and Nari or Narfi; the Æsir changed Váli into the form of a wolf, and he tore asunder Narfi his brother. And the Æsir took his entrails and bound Loki with them over the three stones: one stands under his shoulders, the second under his loins, the third under his houghs; and those bonds were turned to iron. – Arthur Gilchrist Brodeur’s translation
Váli, son of Loki, is otherwise unknown. A variant version in the Hauksbók manuscript of verse 34 from “Völuspá” refers to this event; it begins: “Þá kná Vála | vígbǫnd snúa”, usually changed to the nominative Váli to provide a subject for the verb; in Ursula Dronke’s translation in her edition of the poem “Then Váli | Battle ties twisted”. This probably refers to Váli, the son of Óðinn, who was conceived to avenge Baldr’s death, and it is therefore not unlikely that he bound Loki; but the Hauksbók stanza interrupts the flow of “Völuspá” at this point and is probably based on a different oral tradition. It is likely that this was Snorri’s source and that he interpreted the manuscript Vála vígbǫnd as “bindings from Váli’s battle act” and thus invented a second Váli. In the rather cryptic prose at the end of “Lokasenna”, which seems to be derived from Snorri’s report, Narfi turns into a wolf and his brother Nari’s guts are used to bind her father.