Q:

What cultures have myths related to the origin of aurora phenomena?

Basically, which nations have stories explaining either the Northern or Southern Lights?

A:

In Chukchee mythology, according to Bogoras (1907), the Aurora Borealis is made of the spirits of the people who died a violent death. Some of them are playing soccer in the sky with a walrus head:

The Aurora Borealis is chiefly the place of abode for those who die a sudden or violent death. The whitish spots are the people who died from contagious diseases; the red spots are those stabbed with a knife; the dark spots are those strangled by the "spirits" of nervous diseases; the changeable rays are deceased people running about and playing ball with a walrus-head which is alive. It roars when in motion, after it has been tossed. It wants to strike with its tusks anybody who tries to catch it. Men who have been strangled with a slip-noose at their own request, have honorary places among the spectators; or they themselves may play, but do so in a very awkward manner, because of the rope dangling behind them on the ground.
 W. Bogoras, 1907. The Chukchee – Religion (Part II). Memoirs of the American Museum of Natural History.

This narrative seems to be relatively widespread among Eskimo people since the Inuits from Labrador had similar beliefs:

Only the spirits of those who have died a voluntary or violent death, and the raven, have been over this pathway. The spirits who live there light torches to guide the feet of new arrivals. This is the light of the aurora. They can be seen there feasting and playing football with a walrus skull.
Extract from Aurora: the northern lights in mythology, history and science. 

The soccer game with a walrus head was also rapported by Knud Rasmussen for the Iglulik Inuits:

Here, they are constantly playing ball, the Eskimos' favourite game, laughing and singing, and the ball
  they play with is the skull of a walrus. The object is to kick the skull
  in such a manner that is always falls with the tusks downwards, and
  thus sticks fast in the ground. It is this ball game of the departed
  souls that appears as the aurora borealis, and is heard as a whistling,
  rustling, crackling sound. The noise is made by the souls as they
  run across the frost-hardened snow of the heavens. If one happens
  to be out alone at night when the aurora borealis is visible, and
  hears this whistling sound, one has only to whistle in return and
  the lights will come nearer, out of curiosity.
Rasmussen, K., 1929. The Intellectual Culture of the Iglulik Eskimos. Report of the 5th Thule Expedition 1921-1924.

A:

I hope this doesn't break the rules, but I wrote a post on my blog about both the Northern and Southern lights awhile ago. It covers Inuit, Finnish, Scandinavian, Native American and Australian lore. You might find the references helpful, anyway.
http://earthandstarryheaven.com/2015/02/19/aurora-borealis/
The condensed version:
The Canadian Inuit saw them as dead souls playing football in the sky, and in Maine the Passmaquoddy also saw a ball game in the aurora. Another explanation from the Inuit was that they were spirits who died violently, an idea shared by the West Coast Tlinglit Indians. The Lapps said they were fighting in the air, still fighting after death. A more cheerful view came from the Scots and Norwegians, who saw them as dancers. Both the Maori and Aborigines saw them as fires in the sky. (This is a broad, thematic summary.)

