1. Shaky or unsteady.
2. Out of alignment.
3. Not functioning properly; unreliable.
4. Excessively interested in minor details; wonkish.
As far as I recall, I didn't hear "wonky" used in that 4th sense until very recently. But now I hear it all the time in WPR news stories. Have others heard it used in that 4th sense? Where/when?
According to this site, "wonky" in that 4th sense dates from the late 20th century, and is related to the more common term 'wonk' (someone excessively interested in minor details, especially political details). It looks like the origin of 'wonk' is unknown.
The unsteady/unreliable meaning of "wonky" is from the early 20th century, possibly from Middle English wankel, unsteady. (And no, there is no obvious etymological link between this term and 'wanker'.)
I have (infrequently) heard the term "wonkish" in reference to someone interested in details. That article discussed "wonkish" as well, which appears to be a recently-coined American variant used for the 4th sense of "wonky".