To dream that you are listening to the radio connotes your 'being in tune' with a situation at hand. It further symbolizes awareness and intuition.
Messages you hear through the radio presents a good indication of deep-seated concerns in your subconscious. In some cases, messages you hear through the radio are telepathic messages.
To dream that a radio is turned off suggests you have the capability to contribute to the betterment of a situation. You appear adamant to act on it.