Yasuo and Karma each speak a different, unrelated Ancient Ionian language, given the lack of sound correspondences & cognates (Yasuo's dialect sounds like broken Japanese, parts of it referencing Kiai).
He references and resembles Miyamoto Musashi and/or Haoumaru from Samurai Shodown via his iconic ponytail design shared with these individuals, where in Musashi's case, it is in reference to the common visual design he is depicted with in fictional media.
Haoumaru himself is based on Miyamoto Musashi as well.
Another note in regards to Yasuo is how his Steel Tempest in the Chinese servers is named/dubbed as 斬鋼閃 (Zhǎngāngshǎn, lit. Slashing Steel Flash), which when read in Japanese with the same characters (Zankousen) is exactly the same name as Haoumaru's standing heavy slash and one of his special attacks.
Yasuo's taunt in most of his skins (save for Nightbringer's[S|L] demon form) involves him in-taking fluids from his bamboo flask, then spitting the fluids on his blade to "bless it". This is another nod to Haoumaru via a habit done by him in his home series' battle intros.
Yasuo is an Ionian swordsman accused of treason for allegedly murdering an Elder. He is being hunted down across the island continent under the evidence that the killer employed a wind technique, one that only Yasuo has mastered in the present day.
He crossed paths with Taliyah while on the run, teaching the Shuriman stone mage how to control her powers. When they parted ways, she gifted him a long thread from her handspun wool tunic (the same one he uses to tie his hair up).
Yasuo suspects Riven of being the Elder's killer, as evidenced in interaction quotes with her.
Eventually, Riven confessed to unintentionally killing Elder Souma, whose wind technique shattered her blade and killed him with a stray shard. However, Yasuo admitted to dereliction of duty, for he could have protected Elder Souma had he not left to engage the Noxians.