Nue can briefly summarize cool things that the different kinds of war-gymnasts can do:
Sozev allows the war-gymnast to put unnatural force behind their strikes, heal via touch, lift heavy objects, intimidate others, run tirelessly, sense more acutely, fight off disease, withstand poison, commune with spirits...
Xæmā allows the war-gymnast to befriend an animal companion, commune with a nature spirit, call on animals for aid, take on the shapes of various creatures, manipulate air, manipulate water, 'communicate' with plants (Nue is not confident about what this means so if Lintalai is interested she will need to consult with experts), and supposedly, move on the wind- similar to what shezodza allows, but her impression is that it is more naturalistic, while a zodje moves through the air with as much control over their body as they do everything else.
Shezodza allows the war-gymnast to contort their body into difficult poses, throw objects at high speeds, react more quickly, teleport short distances, cling to nearly any surface, walk on water, "harness the elements" (again, Nue apologizes for not having much detail to offer here), float...
Thievery allows the war-gymnast to dodge nimbly, detect danger, tumble safely, mimic minor spell-casting abilities, predict the future, identify weaknesses, bolster allies and menace enemies (Nue seems least excited about the possibilities offered by this particular type of war-gymnastics), hide unnoticed, move silently, just generally get lucky...
Ranging allows the war-gymnast to befriend an animal companion (Nue thinks this is somewhat different than how it's done in xæmā, but she doesn't know xæmā enough to give a confident guess), understand a specific kind of terrain, aim accurately, take on the natural advantages of animals, hunt a chosen type of prey trivially, produce a healing mist, survey a new environment quickly, recall extensive factual information on the natural world, control plants, and move unnaturally quickly (but only in the wilderness).