I doubt that this is the "original form" of any of the above songs. More likely the chorus of this song was used as one of the "floater" verses that are so common in folk music, and attached to another song.

From Vaudeville, Old & New: An Encyclopedia of Variety Performers in America, Volume 1, by Frank Cullen with Florence Hackman, Donald McNeilly (New York Routledge, 2007), page 962:

Perhaps unwittingly, Pat Rooney exposed some of the fierce racism prevalent among some portion of the Irish American communities in his best-remembered song, "Is That Mr. Riley?":

I'd have nothing but Irishmen in the Police.
Patrick's Day would be Fourth of July.
I'd get me a thousand infernal machines [bombs]
To teach the Chinese how to die,
Help the working man's cause, manufacture the laws.
New York would be swimming in wine.
A hundred a day would be very small pay
If the White House and Capital were mine.

CHORUS: Is that Mr. Riley, can anyone tell?
Is that Mr. Riley, that keeps the hotel?
Is that Mr. Riley they speak of so highly?
Upon me soul, Riley, you're doing quite well.