How did Olohega become U.S territory? And the its effect on the indigenous people?

The Historical development has been given earlier. But recent developments have been more helpful to the Americans (and the Jennings) than to Tokelau. In the 70's, New Zealand and the United States of America, with leaders of Tokelau not fully being aware, reached agreement on the issue of Olohega. A Treaty called Tokehega was signed by Tokelauan leaders and American Representatives. Through that Tokelau "signed away" its claim to Swains while the U.S removed its claim to Atafu.
It is unknown as to what happened to the people on Olohega spotted by the first visitor in 1606.