noun
manner of speaking; way of saying things
Refers to how someone speaks, including tone, phrasing, and overall style of expression.
彼の言い振りには少し棘があった。
There was a slight edge to his manner of speaking.
あの言い振りだと、多分怒っているんだろう。
Judging by that way of speaking, he's probably angry.
話し方 is a more general term for 'way of talking', while 言い振り often carries a nuance about the attitude or impression conveyed by the choice of words.
Compound of 言い (the continuative form of 言う 'to say') and 振り ('manner, style').