The most common misconception about mythology is that one can find a codex that precisely defines what was believed. Religions change over time and space, and belief systems that are not tethered to the written word change even more radically over time and space.

And then ... when one adds the variable of island cultures one adds the factor of isolation, which causes even more radical cultural drift. A language and cultural group as far flung and individually isolated as Polynesia will naturally have many traditions associated with supernatural entities that seem linguistically and culturally connected. Despite the illusion of being similar - even if there is, in fact, a common ancestral belief that these entities might share - the actual beliefs and traditions could be radically different from place to place as they were documented.

Anyone who suggests that they have the definitive description of any supernatural being for any culture is drawing on a written text that may or may not be a reasonable description of the belief system. And even if it accurately describes the beliefs and traditions at the moment it was recorded, it almost certainly does not accurately depict a corresponding tradition in another time and place.

I can't answer specifics about Polynesian traditions and belief systems with authority, but I caution you to use source criticism when considering anyone's "definitive" explanations. The deity Ku could easily be many things depending on the time and place. Even within a single community, supernatural beings were frequently regarded as adopting several - even sometimes contradictory - personas and traits.

Sorry, I started writing something and then took a while to get around to finishing it.

I'll be talking pretty much entirely about Maori mythology, as that's what I know about, I'm also going to be very inconsistent in my use of macrons, so don't use it as a pronunciation guide. Firstly, I second everything u/\itsallfolklore says, and would add a couple of specific cautions about Māori mythology. A while ago I read 'Encounters: the Creation of New Zealand' by Paul Moon, who talks a bit about the difficulties of the written versions of Maori mythology. Aside from some quite basic missionary descriptions (with the obvious problems: they were not very interested in learning, Maori were not very interested in teaching) Maori mythology was mostly collected in the late nineteenth and earlier twentieth centuries, at least a generation after the arrival of Christianity, and certain elements are pretty clearly influenced by a Pakeha-introduced model. The example he gives is a Maori flood-narrative, which has a number of details and motivations (the flood happened because people did not worship Tane) that are clearly influenced by the story of Noah, though the entire narrative is capable of being understood as anti-christian. Pakeha ethnographers were guilty of a lot of a lot of streamlining and 'cleaning up' of their material, and one very important Māori source on religious customs was Mormon (who placed a lot of importance on various theories of Polynesian ethnogenesis). A more basic problem though, is that Maori mythology was intimately connected with their worldview, so that the standardised myths we tell today (mostly aimed at children), as heard by a pakeha audience (without, for instance, the highly personified view of nature that Maori once had) are missing much of the significance they would have held to the original tellers. All that said, here are the basic 'school' versions of the main deities (mostly following Elsdon Best).

The creation of the world, in Maori mythology is understood as a succession of states, often narrated in the form of a whakapapa (genealogy), for instance:

Te Pō (night, darkness)

Te Ata (dawn)

Te Ao (light, world)

Te Ao-tū-roa (longstanding world)

Te Ao Mārama (world of light)

or:

Aituā (calamity, misfortune)

Te Kore (nothingness)

Te Mangu (darkness)

Rangipōtiki (the sky)

Following this, the sky father and the earth mother (Ranginui, and Papatūānuku) emerged. They were locked in embrace, with their children crawling around in the dark between them, until finally they were thrust apart by their son Tane – sometimes with a post and sometimes standing on his head, with his feet against his father. Rain and mist can be considered their tears at their separation.

Tāne (who was worshipped under no less than forty names or epithets) was lord of the forest (as Tane Mahuta), the father of birds, associated with knowledge, and the sun and moon (which he created). He was also the ancestor of humans.

Tu was the war-god (etymologically the same as Hawaiian Ku) and in some traditions the creator of man (though not the Tuhoe ones that Best is following). Given the prevalence of warfare in historic Maori society, Tu was one of the most important gods, and war-parties were under his tapu (no space to explain, 'sacred restrictions'), but he was not actually employed/petitioned (Maori prayer was more like magic) for success in war, for this people would turn to lesser beings, such as Uenuku (the rainbow), Tunui or Rongomai.

Along with Tane and Tu, Rongo was one of the most important gods. He presided over cultivation and crops.

Tangaroa, a sea-god particularly associated with fish, was very close in importance, however a South Island tradition has him as the first husband of Papa (the earth mother), which would put him as one of the principal gods.

The other main 'departmental' deities that Best lists are Tawhiri-matea, god of winds, who stayed with his father Rangi after his parents were separated; Haumia the fern-root (a very important food); Whiro, who was associated with darkness evil and death; Ruaumoko, youngest child of Rangi and Papa, and still at his mother's breast (beneath the earth) where he causes earthquakes and finally Uru-te-ngangana who is a being (or possibly two) associated with light and the heavenly bodies. There are also, obviously a huge variety of other gods, right down to very local spirits or personifications.

One interesting problem is 'Io'. Early twentieth-century literature holds that he was the supreme creator god, however there are no early references to him (though knowledge of him was supposedly restricted) and it's possible he was completely invented, or heavily altered, under the influence of Christianity, and then promoted by ethnologists wanting to give the impression Maori had 'higher' religious conceptions. There are a few karakia (incantations, prayers, hymns) that were collected that make reference to Io, and seem to be quite old, so it's possible that he was a real concept, though maybe local.

Sources/further reading.

I used the Te Ara page on Māori creation traditions.

There are several relevant old books online.

Elsdon Best's Maori Religion and Mythology Part 1 and Two