An affectionate name for "grandmother," (esp. a somewhat cold, possibly drunk grandmother with aspirations of social standing.)
On the television show Arrested Development, Maeby Fünke and George-Michael Bluth call their grandmother (Lucille Bluth) "Gangy" in many instances.
The etymology is unclear but it's frequent use in context makes the meaning clear. The spelling "Gangy" seems to be the generally-agreed upon spelling on Wikipedia, IMDB, and most TV sites.
George Michael Bluth: "Was that Gangy
who was just… " (slips on Lucille's spilled martini and falls)
Michael Bluth: "You all right? Sorry. Your grandmother had a little accident here."
George Michael Bluth: "Oh. Does that means she's gonna have to come live with us?"