This is dads favourite song! The song is "Celery Stalks At Midnight" by the Will Bradley Orchestra.
This version was recorded on January 17, 1940 by the Will Bradley Orchestra with drummer Ray McKinley exclaiming that "Celery stalks along the highway".
McKinley was also the co-leader of the band. The tune was written and arranged by George Harris. Rumor has it that it was originally written by Raymond Scott and merely modified a bit by Harris. In the Bradley-McKinley band was Peanuts Hucko on clarinet and tenor.