How to wire this fan?
The research I've just completed indicate that the motor may be called a split phase motor, although there's enough ambiguity in the search results to be uncertain. The indication I've found is that each of the four leads is an independent power lead. A four-position switch, typically rotary, with the common to power and each of the four leads attached to the switch will give you speed control. Prior to purchasing the switch, you can test this by connecting your ground and neutral and making contact with each lead with your 110v source line.

There's no indication of the need for an external controller appropriate to a stepper motor.