My school faculty members put on a band that played oldies and one of them was really catchy and I wanted to find it. It has the lyrics "my my my my" and "I'm movin' on" occasionally! Please help! Google searches didn't help.
Are you sure it's exactly I'm movin on multiple times?
If not I think you mean Catch Me Daddy, by either Janis Joplin solo (1982) or originally Big Brother and The holding Company (1968). That song was one of the two that latter band, were Joplin was the lead singer of, was best known for.
To be precise both lines only ones used:
You know, I want ya, need ya, I gotta have ya 'Cause I want ya need ya, 'cause I gotta have ya 'Cause this my-my-my-my-my-my-my-man My-my-my-my-my-my-my-man now
And the other:
Cold sheets made me realize, catch me, daddy, 'cause I'm movin' on
Come on up, come on up, come up, I've got to move on
Oh, I guess I might finally walk in there I gotta, gotta, gotta, gotta move on
Note: I also used Google Search, specifically
intext:lyrics "my my my my" "movin on" As you can see in some form Stevie Wonder and Led Zeppelin were among candidates, just not both lines ^^