As defined by Cosmo or Sykes (Joe Pantoliano and Daniel Roebuck respectively) in the 1993 movie "The Fugitive". In a conversation in the Federal building, Cosmo, Sykes and Sam Gerard (Tommy Lee Jones), the situation with Dr. Richard Kimble (Harrison Ford) is described as Hinkey, meaning that it is strange or unusual. Gerard exclaims that he does not know what that means and doesn't want them using words around him that he does not understand. Hence, if something, or someone is hinkey, it is strange and/or unusual.
Seeing the sun shine while it is pouring down rain is hinkey.
He was acting hinkey, I think he's on something.
Don't get hinkey with me, mister!
Doesn't that seem a bit hinkey?