"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
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. [Wyclif, 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.