A core element of this sort of quasi-anthropological fiction is offering the reader a visceral sense of another time and another culture. Ulysses does it for Dublin in 1904, Mary Renault does it for Ancient Greece, Patrick O'Brian for the Napoleonic-era Royal Navy. It's a history that involves not cataloging of events, or detachedly describing what That Age involved, but rather conveying through a personalized account what a different time and way of thinking were like on an experiential level. Science fiction and fantasy greats become greats because they succeed at this.
So how can Lafferty possibly hope to write at that level of intimacy about Native Americans who were transported to and lived in Oklahoma before he was born? Well that's an interesting question.
Lafferty grew up in heavily native Oklahoma in the 1920s with Choctaw playmates and classmates. He lived in Indian country throughout his life. He was also an obsessive reader and polymath and appears to have read almost literally every primary document concerning native Americans in Oklahoma during the 1800s (court records, treaty accounts, biographies, interviews, depositions, etc).
So Lafferty knew Choctaws, and was learned about Choctaws. But can we take him seriously as a conveyor of a personal 19th century Indian experience? Count me skeptical. Still, at least one eminent Cherokee historian (Geary Hobson) has held up Okla Hannali as an "excellent fictional rendering of American Indian views (and in this case more particularly, the Choctaw view) of American history and Indian Territory during the last century," so what do I know?
What I can verify is that Lafferty succeeds totally in conveying a version of a culture and mentality that ring totally true and truly different. The main character, century-spanning Okla Hannali is huge, frank, multi-talented, funny, pragmatic, fatalistic, dogmatic, hard working. The Choctaw were/are farmers, and they approach life like farmers. Crops fail? Keep working, add another rose bush to the front walk. Hannali operates in a scene of unimaginable tragedy, but doesn't approach it that way. After being relocated to Oklahoma he gradually builds a huge, multifarious house and gathers an enormous multi-generational, multi-ethnic family around him.
A quality of Lafferty's writing is a sense of fable, or tall tale. This quality carries over to his non-fiction work (in which I include Okla Hannali even if parts of it are not, strictly, nonfiction). At times it's hard to tell when Lafferty is exaggerating, and he definitely delights in exaggerating -- ("Hannali had now attained his majority. He was the best farmer in the Choctaw country. He was a mule man, a corn man. He was now in actual charge of all the Innominee production.").
This all lends an air of unreality to the narrative, which is effective and is intentional in some sense--although it's not like Lafferty crafted it for this book, it's just how he writes. I can't imagine any experience more unreal than being an Indian in those times. A Laffertian telling might be the only way to capture the mixture of absolute horror combined with phlegmatic living of lives as cultures crash into one another.
A couple of final notes:
(1) I was reading the autobiography of Ulysses S. Grant at the same time I read this. It's hard not to feel proud of Abe Lincoln's Union reading that book. Okla Hannali is not written like a tragedy, and I think it's better for it, but it's impossible to escape the unrelenting vicious brutality engaged in by the US government. Even the goddamn Civil War was used as a free ranging excuse to butcher and exterminate Indians by both sides. The enormity of these events cannot be overstated, and Okla Hannali presents them unstintingly. It's also worth noting just for context that Lafferty was no bleeding-heart academic with an agenda of highlighting oppression. He was a rock-ribbed conservative, WWII combat veteran.
(2) I think Okla Hannali is probably the most accessible Lafferty book I've read, but as a result it lacks a lot of the wonderful wildness and bizarre sidethinking of his other work. It's not at all my favorite. But still good.