Whether they have any extant function or not, they have lost their former function and in that sense they do fit the definition of vestigiality. Vestigial structures are often called vestigial organs, although many of them are not actually organs.
There are quite a few birds famous for doing ritualized mating dances, so I would only list 5: The Red Capped Manakin, The Black-footed albatross, The Western and Clark's grebe, The Superb bird of Paradise, & The Victoria's riflebird.
Native American Oriole Mythology. Orioles are not very important birds in the folklore of most Native American tribes. Like other small birds, they sometimes appear in folktales as symbols of humility and industriousness. The Hopi see the oriole as a directional guardian, associated with the north.