There is no single origin story of Tokelau, perhaps because Tokelau is composed of several atolls. Some of the origin stories are all about the atolls while others are concerned with only one or two of them.
There is an old story that is told about the origination of the name Tokelau. Tokelau is no longer called the Tokelau Islands, but has simply been named Tokelau by the people who first settled the three atolls. They tell the story of how Lu, a magical child raised the sky and placed the winds in the directions that they now blow. The name Tokelau relates to all three atolls and means northerly wind in the Polynesian language.
Other stories tell of how the atolls are differentiated from one another. For example, there is a story that identifies fish with each atoll: the Kanaelauvaka (Tiger Shark) identifies with Olohege (now part of American Samoa), the Mago (Shark) identifies with Fakaofo, The Puhi (Eel) identifies with Nukunonu and the Tifitifi (Butterly fish) identifies with Atafu. In this story the Kanaelauvaka is a predatory fish which is overcome by three others: the Mago of Fakaofo attacked its head, The Puhi of Nukunonu attacked its body, and the Tifitifi of Atafu attacked its tail. This differentiated the atolls from one another and gave each atoll its uniqueness.
In the same manner, there is an old song that identifies foods with the four atolls; pale coconut meat (dried slowly with an unbroken shell) is identified with Olohega. Rich oily coconut is identified with Fakaofo, the fruit of nonu is identified with Nukunonu, and the skipjack fillets are identified with Atafu. It emphasizes the different features of each atoll, but has no real mystery of origination in it. The song is as follows:
Each atoll is also identified with particular spirits, which competed or tricked one another. The story of Hemoana and Fenu is the most widely known tale about these spirits. Finally there are stories about the origins of the people of the atolls; each atoll has its own story, which would seem to indicate that the people of Tokelau did not arise from a single source, but rather that the people of each atoll had their own origins.