Here's the catalog entry from The Indiana University Sheet Music Collections:

Title: INKA DINKA DOO
Composer: Durante, Jimmy
Lyricist: Ryan, Ben
Performer: Jimmy "Schnozzle" Durante
Publisher: Irving Berlin, Inc.
Place of publication: New York
Date of publication: 1933
Call Number: M1 .D48 Box: 032 Item: 055
Performance Medium: Piano, Voice and Chords
Larger Work: Joe Palooka
First Line: What is that haunting refrain you hear in the air?
Chorus First Line: Inka dinka doo, a dinka dee, a dinka doo.
Genre: Popular song

I would bet that the first set of nonsense words in the verse are an allusion to an older song, CRAZY WORDS, CRAZY TUNE, from 1927, which contains the words "Vo-do-de-o," etc.