斡 alone is rare in modern Chinese — you'll almost always see it in the compound
斡旋 (wòxuán, "to mediate / use one's good offices"), a staple of diplomatic and legal news. Originally
斡 meant "the handle of a ladle" (Shuowen 《
说文》) — that which turns to scoop. The metaphor: the diplomat is the handle that turns the situation.