Actually the proper term is "oogedy oogedy boogedy". Waltrip popularized it, since he had the forum as a TV broadcaster, but the term originated on the NASCAR circuit years before Waltrip mentioned it on TV. To find who exactly coined it would require further research.
Given Waltrip's sort of proprietary attitude towards the term (he says every time a race starts), I suppose it's possible it originated in the Waltrip family itself, which goes way back in NASCAR and might be considered NASCAR aristocrats, so to speak. Aristocratic rednecks, if you will.
OK...I got the answer. Oogedy-boogedy, or, as I said earlier, more properly “oogedy oogedy boogedy” is a misspelling of Waltrip’s original phrase “boogity boogity boogity.” Waltrip coined the phrase in its NASCAR context. He came up with it when he was a driver to liven up radio communication with his pit boss at the start of the race. But the phrase itself actually came to Waltrip from a 1960 doo wop song, “Who Put the Bomp” by Barry Mann.