What I think is a proof that it is not possible if the wizard can tell truth and lies and teleport, when he does not know the answer to questions
EDIT: It has been brought to my attention that through paradoxes, this question is solvable, however, that doesn't quite fit. Regard this as a proof of the above, with the law of excluded middle
not spoilered because this is to stop people trying to solve impossible question
In any case, the only one we need to work to find is the wizard; the others are easily distinguished
We can only pin down the wizard to "this guy is not wizard". If we ever get the wizard to remain silent, we win (because we can get him), so we assume wizard will not remain silent. We can force the wizard into two possibilities, by using "Would the Wizard say no to this question?" (wizard must lie or be silent), or its inverse, and we can then find the knave using this, but it doesn't matter, because we can only pin him down to these two, we cannot question the definite non-wizard, because he can't know if the wizard swapped places when we asked "Would the Wizard say no to this question?" to someone, and we cannot ask the possible wizards, because then they could lie OR tell truth, and then swap places, but also not swap places. So, it is not possible to definitely find the identities if the wizard can teleport given an unknowable question