Movie "The Halls of Montezuma" (1950) in context of USMC, Pacific, 1945:

                As I was sitting in O’Reilly’s bar,
                Listening to tales of blood and thunder,
                Came a thought into my mind,
                “Why not love O’Reilly’s daughter?”

                Fiddly-eye-o, fiddly-eye-ay,
                Fiddly-eye-o for the one-eyed Reilly [sic],
                Rub-a-dub-dub, kiss and hug,
                Rub-a-dub-dub, love on!
                
                I grabbed that sea-witch by the hair...

Tune is essentially "Polly-Woddle-Doodle."


Daily Telegraph (Sydney, NSW) (Aug. 19, 1951) (review of the movie):

"A touch that might be missed by many is the singing of about half a verse of the age-old ditty 'One-eyed Riley's Daughter' by a marine.

"This ditty is as well-known to marines as the famous parody on 'Colonel Bogey' is known to Australian troops."