R.E.M. - Oddfellows Local 151 (HQ) - YouTube
"Peter Buck said that the "Oddfellows" were a social organisation, "just like the Mooses or the Shiners", with lodges all over Athens.
He also explained that the song was about the old winos who lived near Michael Stipe. They drank all day and slept in their cars, so the band called them the "Motor Club". Buck remebered that one of them really was known as Pee Wee. The name Oddfellows is used ironically to suggest that this assortmnet of drunks were like a fraternal society.
Stipe himself said the song was a debunking of the "Southern folk" myths he had written for "Fables of the Reconstruction" (e.g. Wendell Gee, Old Man Kensey). In other words, the quaint eccentrics of his earlier songs turn out to be nothing more than sad old drunks."
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R.E.M. - Oddfellows Local 151 Lyrics | SongMeanings