I think Esther picked this up from a song called “Old McDonald Had A Band,” which is on one of her Raffi CDs. I have begun referring to music as “EIEIO” as well (e.g. “Callie, do you want to hear some EIEIO? How about The Life Pursuit?”).
(Note: there was an actual band called EIEIO in the ’80s, but we don’t own their records.)