I think the use of rhubarb goes further back than radio but I have no references for that.
The vaudville expression "stuck in the corn" makes sense as most of the performers were trying to get of the rural (corn)circuit and into the supposedly more sophisticated and better paying big city clubs. But where does "being a ham" come into it? I know it pre-dates Miss Piggy.
Another related term would be "he looks pretty seedy" for scruffy or "gone to seed."