I see the Omaha Tribe as being very similar to other Plains Indians Tribes that made up that area of the country.
Like other Plains Indians they were hunters and gatherers and followed the buffalo every chance they got. This was no different than other tribes like the Sioux or the Dakota Tribes.
What I find interesting is that the Omaha Tribes were not members of the Sioux Nation. The Sioux Nation itself consisted of various factions of the Sioux Tribe and controlled a large portion of this area. In fact, there were very few tribes in this area of the country that were not affiliated with the Sioux and the Omaha was one of them.
The Sioux were very powerful and a danger to fight and it seems like the Omaha Tribe was a strong people that did not run away from a fight, but braved it out and saw other ways of settling differences. Their game of touching their opponent instead of killing them is an example of their bravery and I find it amazing that they would do this against a tribe like the Sioux.