Whether the fan has a dedicated oscillation motor or is driven by an extended shaft from the main motor, there is usually a button or switch to disengage the oscillating function. If this no longer has any effect the only cure is to dismantle the machine until the fault is discovered and then if a repair is possible - repair it...

Most domestic fans have no spare part support, mechanisms have a limited life and if "handyman" repairs aren't possible it is considered a throw-away item.