It's an original, not a parody. However, originals are often in a song style of another group. This one is like Guns 'N' Roses
That is not a Weird Al song.
The original recording of the song Callin' Baton Rouge was recorded by the Oak Ridge Boys in 1978. The song has been covered by many artists. Great song.
Weird Al NEVER made a song about Barney on fire.
Callin out by Lyrics born
Avril Lavigne's Complicated
its a parody of "Ridin" by Chamillionaire
"I Want it That Way" by the Backstreet Boys
Weird Al never does a parody of any song unless the musician who wrote that song gave him permission. So he was clearly not punished at all for that parody.
"Piano Man" from Billy Joel.
He made a parody of "Bad" by Michael Jackson.
The lyrics to Callin' Baton Rouge are available online at SongMeanings, MetroLyrics, and LetsSingIt. The song was written by Denis Linde and the original recording was by The Oak Ridge Boys.
Weird Al doesn't have a song called "beer song"