I should have found this first, but, here it is now: a site with info about all these songs: http://www.bluegrassmessengers.com/braying-mule--uncle-dave-macon.aspx

Dave Macon's "Go Along Mule" is an adaptation of Henry Creamer & Turner Layton's song "Whao Mule," but that song was actually taken from black traditional singing (source: http://www.fresnostate.edu/folklore/ballads/LoF231.html)

That site gives Braying Mule as an adaptation of Thomas Westendorf's "Johnson's/Thompson's Old Grey Mule," and his version of Greenback or Whoa Mule as an adaptation of W.S. Hays' version

Macon's "Braying Mule" is more like most other people's version of "Johnson's Mule."

Hopefully now that all the confusing names are sorted out, I can get into the last one.

BRAYING MULE
(Thomas Westendorf)

Johnson had an old gray mule, he drove him to his car
He loved that mule and the mule loved him with all his mule-ish heart
Johnson knowed when the rooster crowed, day was gonna break
He rubbed him down with a big corn cob and curred him with his rake

CHORUS
That ole mule went [*insert mule noises*]
While Johnson curred him with his rake

His skin was good as purchase, hooves were hard as lead
He'll raise you like a feather, too, and raise you on your head
He would kick as quick as lightning, he had an iron jaw
He's just the thing to have around to tame your mother-in-law

CHORUS

He backed himself into a mule pond and kicked the ears from a frog
Killed seventeen Chiner-men and swallered a yeller dog
He kicked the feathers from a goose and broke an elephant's back
He stopped a Texas railroad train and kicked it off the track

CHORUS

They hitched him to a cart, all limp and lame was he
We hitched him up to that cart to see how he would be
He kicked three days and couldn't faze, he got so short of breath
He swallered one'a his left-hind legs and choked himself to death

CHORUS

Transcribed by ear. Occasional reference to here: http://www.topix.com/forum/who/pete-seeger/TAIDM7129QRQO2AGC