"shaky, groggy, unstable," 1919, of unknown origin. German prefix wankel- has a similar sense. Perhaps from surviving dialectal words based on Old English wancol "shaky, tottering" (see wench (n.)).
Entries linking to wonky
wench n.
late 13c., wenche "girl, young woman," especially if unmarried, also "female infant," shortened from wenchel "child," also in Middle English "girl, maiden," from Old English wencel, probably related to wancol "unsteady, fickle, weak," from Proto-Germanic *wankila- (source also of Old Norse vakr "child, weak person," Old High German wanchal "fickle"), from PIE *weng- "to bend, curve" (see wink (v.)).
The wenche is nat dead, but slepith. [Wycliffe, Matthew ix.24, c. 1380]
In Middle English occasionally with disparaging suggestion, and secondary sense of "concubine, strumpet" is attested by mid-14c. Also "serving-maid, bondwoman, young woman of a humble class" (late 14c.), a sense retained in the 19c. U.S. South in reference to slave women of any age. In Shakespeare's day a female flax-worker could be a flax-wench, flax-wife, or flax-woman.
wonk n.
"overly studious person," 1962, earlier "effeminate male" (1954), American English student slang. Perhaps a shortening of British slang wonky "shaky, unreliable," or a variant of British slang wanker "masturbator." It seemed to rise into currency as a synonym for nerd late 1980s from Ivy League slang and was widely popularized 1993 during the presidency of Bill Clinton. Tom Wolfe (1988) described it as "an Eastern prep-school term referring to all those who do not have the 'honk' voice, i.e., all who are non-aristocratic."