The most famous piece of oral history in my region concerns the foundation of the Haudenosaunee, the Iroquois Confederacy.
It happened in a time when the Five Nations were fighting among themselves. Cannibalism was rampant, particularly by the chiefs and their warriors. Everyone else was nearly starving because the fields were constantly being burned.
Into this mess came Dekanawida, the Great Peacemaker. In the most well publicized version of the narrative, the Peacemaker was originally a Wendat, from across Lake Ontario. In other versions, he was a member of one of the Five Nations. Regardless, he undertook a mission to end this era of senseless war and cannibalism.
Early in this mission he encountered Jigonsaseh, a Seneca clan mother. She maintained a longhouse on one of the main trails through the land of the Five Nations where she fed and sheltered warriors regardless of their allegiance in exchange for the protection of her community. She was also a strong proponent of a new crop, maize, the adoption of which she believed would help further the cause of peace. Since their goals aligned, the Peacemaker and Jigonsaseh blended their ideas together. The Peacemaker adopted maize as a tool and symbol of peace, and Jigonsaseh brought the so-called "maize faction" in line with the Peacemaker's message of the Great Peace (to which, she is also credited with adding various provisions concerning the rights and responsibilities of women).
A brief diversion: in some version of these events, Jigonsaseh is fused with an otherwise nameless Mohawk clan mother that sided with the cannibal faction. This creates an all together more villainous version of Jigonsaseh.
Continuing on his mission, the Peacemaker came to Onondaga, then ruled by the powerful and belligerent Tadodaho. At the time, Tadodaho was unwilling to hear the Peacemaker's proposal, as he profited too greatly from the continued violence. However, Hiawatha, who was one of Tadodaho's war chiefs, was receptive to the Great Peace. He had either already attempted one coup against Tadodaho or would do soon after meeting the Peacemaker. Either way, the attempt fails and Tadodaho has Hiawatha's family killed in retaliation.
While Hiawatha is in morning, the Peacemaker employs the Condolence Ceremony for the first time. The Condolence Ceremony is a major aspect of the Great Peace, as it provides an alternative outlet for grief and restitution without resorting to the endless cycles of Mourning Wars that currently plagued the Five Nations.
Soon the Peacemaker and Hiawatha leave Onondaga behind and head east into Mohawk territory. After less than friendly welcome and a miraculous escape or two, the pair win the trust of the Mohawks and are adopted into the nation (which likely accounts for one version of the narrative that says they were both Mohawks).
Hiawatha proves to be a huge boon for the Peacemaker's efforts. While the Peacemaker has the plan, he lacks Hiawatha's charisma. But putting their skills together, they make a great team. Soon they've converted the Mohawks, and from there the pair heads west again to get the other nations on their side against Tadodaho. Even the other Onondaga chiefs eventually convert, though Tadodaho remains a force to be reckoned with and no one is quite willing to challenge him again just yet.
Other than the Tadodaho, the last hold outs are the Seneca. Jigonsaseh had been working in the area but the cautious Seneca chiefs weren't yet ready to commit. A council was held when the Peacemaker returned with Hiawatha, and after some debate and a solar eclipse to provide a sign for the more hesitant chiefs, the Seneca finally agreed to join the Great Peace. The Five Nations became the Haudenosaunee.
But there was still Tadodaho to deal with. The Peacemaker, Hiawatha, and Jigonsaseh led what was essentially a peaceful protest against his warmongering. They wanted him to accept the Great Peace, but to sweeten the deal (as he still commanded enough power to be a threat), they offered him a position as first-among-equals. He would serve as the chair of the Grand Council. Confronted in this way, powerful yet bereft of allies, Tadodaho relented and accepted the Great Peace.
The Peacemaker convened the Grand Council for the first time in Onondaga and there composed the Great Law of Peace. The various leaders of the day became the fifty League Chiefs (including Hiawatha and Tadodaho). We know the names of all of them because their names became the titles that been passed down from generation to generation ever since - except for Hiawatha's seat, which was retired after his death as no one was seen be a worthy heir to his legacy. Jigonsaseh, meanwhile, became the chair for the women's council, and we know many but not all of the names of the clan mothers who served with her because they have likewise been passed down through the generations (unfortunately, the earliest full list we have of them now comes from a time when English personal names were becoming common and the list is a mix of the honorary titles and personal names).
There have been various attempts to date these events, made somewhat complicated by a tendency in Iroquoian oral history to smooth out the rough edges of history to make a more consistency narrative. The three major lines of evidence for dating have been the the introduction of maize to the region, the solar eclipse, and the number of Tadodaho that have served on the Grand Council. These dates point toward the early part of the second millennium CE, with the best possible eclipse occurring in 1142. However, some archaeologists (Dean Snow in particular) favor a later date (well into the 1400s) based on an uptick in discernible archaeological violence at that time that could correspond with the internecine warfare between the Five Nations that preceded the Peacemaker's mission. Personally, I favor the earlier date.
Events, yes, raids and battles, yes. Major battles? perhaps - depending on the definition. Many North American cultures have oral history that extends back several thousand years - some (many athabascan groups) are argued to go back up to ten millenia (back to megafauna).
Where I grew up - (Gitksan territory) oral history preserves the destruction of the ancestral village/city to what are today 4 languages, and then goes back before that to larger floods in the area. It includes volcanic erruptions, and the like, including dark periods of incoming raiders from the north, being conquered, and a liberation raid against the invaders that is supposed to have taken something over a thousand years ago.
Where I live now, oral history goes back a long ways as well, and includes stories about epic battles between ----- supernatural powers and mountain size ice giants who were slowly driven back to the north, following which the ancestors descended down from above into the valley. The extent to which this reflects the retreat of the ice age and immigration at that time is debateable, but archaeological evidence goes back over ten millenia.
Now to major battles. Major immigrations have happened, yes, and wars have happened, but as to major battles involving thousands of individuals? it's hard to say. I know that in this region (pacific northwest) of the world, it was only the increase in wealth brought on by the fur trade that allowed individual chiefs to gain enough power to bring together larger groups of men for large scale raids. While very likely large battles may have happened in the more politically unified communities in the south, my impression from reading oral histories is that they were not as common in this area, though I would love to be corrected on this point.
hi! you may be interested in some of these earlier posts
Have there ever been any Eskimo/Inuit conquerors/emperors/kings?
Is there any records of Native American v. Native American battles?
What was war like in the Pacific Northwest before European contact?
What was the largest pre-Christopher Columbus war between Native Americans we know of?
What are some examples of wars fought between Native Americans after European contact?
Was there ever a "war" between Native American tribes before European settlement?
Related question, if I can piggyback. I recall reading in the (even then) outdated books of my youth about the destruction of the Cat People or Erie. What does history say today about that people and its (possible?) destruction?