"I heard your father speaking on the radio."
Translation:Oí a tu padre hablando en la radio.
As far as I can tell in research, the difference between a mechanical radio and a radio program is slight. And yes, por la radio would mean on a radio program. Por el radio would mean something like "through the radio". Native speakers would be good to ask, might tell you it's the same thing.
As far as I can tell, "el radio" is the device (the actual radio machine) and "la radio" is the medium/programmes transmitted on "el radio"