UBUweb has circa 1960 recordings of Nash reading his poems, accompanied by custom composed background music, on their site .
On the BBC site they have recorded excerpts from a Halloween, 1964 recording of their interview with Ogden Nash at the links below:
BBC Recording, You and Me and P.B. Shelley by Ogden Nash
The influence of James Joyce, picking and stealing and rhyming techniques 2 min 0
Women 2 min 7
Other people's descriptions of him 1 min 25