No, its form is an amalgam of those four, appearing in part as all but actually having the shape of none. This is, in fact, what the page says: "つかず" is a somewhat archaic negative form of "付く", roughly "without adhering to".
It is written:Its cry is not quite that of a beast's......nor a bird's, nor a child's.With a form, which is not quite a monkey's, nor a tanuki's, nor a tiger's, nor a snake's.While there is not a human left in the village that does not know me...At the same time, there is no one who knows of my true form.