Norse mythology in the sense of what was written down in the texts, primarily the Eddas, in 13th century Iceland, are quite different things than the actual pre-Christian beliefs. The Eddas were not scripture, they were not written for the sake of preserving the actual religious cult but rather the literary tradition. The stories they record were the ones which Christians had seen fit to continue to pass down, and some of which were amended if not outright composed during the Christian era. (not that single 'canonical' versions the folklore ever existed) See e.g. the thread Why did Snorri write the prose Edda? on that.

So for instance, while Loki is one of the most prominent gods in the mythological stories, he is a non-entity as far as worship is concerned. There are no objects with religious invocations of him, no place-names indicating cult sites named for him. Although early pioneers of the topic like Jacob Grimm (Deutsche Mythologie 1835) sought Indo-European origins for Loki as a fire-god, the consensus today is that he was a late addition to the pantheon (9th century at the earliest). The Viking Age contexts where he does turn up (e.g. the Gosforth Cross) tend to be syncretistic, mixing Christianity with Norse folklore.

Loki is but one example; there are other prominent Eddic gods who are little represented outside those texts, and vice-versa. In terms of place name evidence, Ullr had more cult sites devoted to him than either Odin or Thor did, (Brink, 2007) yet Ullr barely gains a mention in the Eddas.

In the case of Vili and Vé, there is no evidence of any cult at all. And hardly any reference to those words as names ('vili' meaning 'will' and 'vé' (OWN) or 'ví' (OEN) meaning a cult site/sanctuary). No place names, no objects using those names in invocations and such.

They were not popular literary characters either; there is only a single reference to these names in the actual skaldic literature that dates back to the Viking Age. That is in Lokasenna (verse 26), where Loki accuses Frigg of sexual impropriety with the two. And that is all. So there is no explicit or implicit statement that they're Odin's brothers nor that they had any particular cosmogonic role. Even given the aforementioned caveat that this is not scripture, Lokasenna is doubly problematic as a source since even 'in-story', these are insults by a Loki provoking people, and not necessarily facts. Indeed, Loki also accuses Idun, Gefjon and especially Freyja of sexual impropriety so it's not so original either. (to be frank, Lokasenna isn't the best of skaldic poetry)

It is in the Gylfaginning, in Snorri Sturluson's Edda, composed in 13th century Iceland in a society that'd been converted for multiple generations, that the names turn up again. Verse 6: "Hét einn Óðinn, annarr Vili, þriði Vé, ok þat er mín trúa, at sá Óðinn ok hans bræðr munu vera stýrandi himins ok jarðar." - One was named Óðinn, the second Vili, the third Vé, and it is my belief, that Óðinn and his brothers are the rulers of heaven and earth (my transl.)

This is not he same trio, nor exactly the same role, as in the older skaldic poem Völuspá, where it is Óðinn, Hænir and Lóðurr (who are not claimed to be brothers) who create man. (However, Völuspá and its cosmology is not so old that it is without Christian influences)

Snorri knew about Völuspá, so it is possible that these were the same figures in his opinion. But Snorri was a Christian; and his description here is probably his own and not ancient tradition (considering the use of the Christian idiom 'heaven and earth'). Snorri believed the old Norse gods had in fact been actual human kings who'd been wrongly elevated to god status due to their power and skill in magic. (euhemerism)

This way of explaining pagan gods (euhemerism) was common thing in the Middle Ages, and had been done with the old Greco-Roman gods. Another common practice (I once listed some here) was claiming Trojan descent after the Roman model of the Aeneid. Snorri engaged in both these practices, and they're found in the same texts that mention Vé and Vili: in Gylfaginning (which equates Hector with Thor) and in Ynglinga Saga, in Heimskringla. The latter is partially based on the legendary kings of the older Ynglingatal but the first parts are likely Snorri's creation and tie into his theory of the Æsir coming from Troy (equating Asia with Æsir in a kind of history-by-folk-etymology not uncommon in medieval historiography).

Here, the Æsir are living in "Svíþjóð the Great", a fictional predecessor state to Sweden (Svíþjóð) somewhere around the Don Delta on the Black Sea. They meet up with the Vanir, who are from Tanais, a name Snorri derives 'Vanir' from in another etymology. In this part (chapter 4) of Ynglinga Saga, Snorri used Lokasenna as a source, claiming claiming the Vanir came to the Æsir as hostages (off an accusation at Njord in verse 34) and that Njord had been married to his sister when among the Vanir as it was their custom. Which explainins an accusation of incest in Lokasenna 36.

Indeed it has been suggested by Rudolf Simek (RMN 01, 2010) that the entire Æsir-Vanir story for which Ynglinga Saga is the main source, and the distinction of those gods into two groups, was Snorri's own invention, based off a misreading of the term Vanir as referring to a distinct group, when the skaldic sources make no real claim to that.

In any case, the mention of Vé and Vili in chapter 3 of Ynglinga Saga also match this pattern in that part of the story of stating rationales for insults from Lokasenna; it is explained that they ruled in Odin's stead (Odin the 'actual' human king here, not the god) when he was away, and once he was away so long that they didn't think he'd come back and so they split his wealth among themselves and his wife Frigg married them both. But Odin returned and took his wife and property back.

Now if we consider Ynglinga Saga as being in part Snorri's 'historic' rationale for Lokasenna, then it readily suggests itself that this story set out to explain how these otherwise-unknown figures Vili and Vé could've gotten away with having had sex with Odin's wife Frigg. Obviously that kind of thing doesn't happen to god-kings (much less actual gods). Obviously Loki could've been lying, but we've already established Snorri seems to have taken Loki's insults seriously and sought to explain them. The story is constructed in such a way - probably the only way conceivable to Snorri - in which such a thing could happen without it being a dishonor to Odin, which of course would not be compatible with his godlike-king status. Therefore Snorri figured they must've been his brothers, and included a mention of that in Gylfaginning. (where he hedges his statement uncharacteristically; claiming he thinks this)

So rather than being major figures who faded into the background by the time things were written down (like Ullr), evidence is more on the side of these being minor figures elevated to godhood by Snorri a few hundred years after the Viking Age. There's no cult of them attested. The only pre-Snorri reference is in Lokasenna, which again says nothing about whether they're gods or anything, other than that they had relations with Frigg. After that they turn up in Ynglinga Saga, where Snorri was seeking to give a historic explanation for the insults in Lokasenna, which he apparently took both literally and seriously.

Since /u/Platypuskeeper has so excellently answered your main query I'd like to comment on what seems like a misconception of the nature of Vedic religion. Vedic religion was not really proto-Hinduism, rather the development is much more complex. Brahma does not appears at all in properly Vedic sources, only in very late addenda to the Yajurveda, postdating, for example, early Buddhism.

Shiva ("fortune-bringing", "kind") appears in the Rgveda as the dual nature of the fierce (but minor) trident-wielding storm/wind god Rudra. Shiva as we know him would develop and eventually emerge in a syncretic context, conflated with various other deities, affected by Hellenic, Buddhist, Dravidic and other influences. For instance, in Kushanite art (which took influences from Greek, Mesopotamian, Iranian, and Chinese religion, as well as Buddhism) we find Shiva depticted as Oesho, a triune deity with the symbols of the trident (Rudra's - fierceness? Destructive?), Club (Indra's - creative? Enforcing? Protective?) and jar (auspiciousness of Shiva, symbolizing the gift of wealth?).

Vishnu ("Unbindable, all-pervading") seems to have originated as an aspect of the hero-strongman-creator Indra who fashiona the raw, unpolished cosmos through brute strength. Indra would go on to abaorb aspects of Varuna and Mitra, gods of sustaining the world and upholding the law. Again widespread conflation occured with these deities especially with the entrance of foreign dynasties, with for instance Mitra, Apollo, Zeus, and even the Maitreya Buddha sometimes being conflated, which is what gives rise to the very complex and manifold natures of Hindu deities as they continue to develop into their familiar forms in the middle ages.

All this is to say that the notion of a parallel cult of Odin/Vili/Ve is preposterous, given how late the development of the Brahma, Shiva and Vishnu cults as we think of them is.