Third Rail - Run, Run, Run
Strawberry Alarm Clock - Incense and Peppermints
Small Faces - Itchycoo Park
The Hombres - Let it All Hang Out
I had never heard "Run, Run, Run" until I read your post and then played it on Youtube. An oddball, indeed. The other oddballs were hits on our local Top 40 stations.
A couple more oddities from that same period:
Reflections--The Supremes
My World Fell Down--Saggitarius
There was a bit of bubble gum in that era, Tommy Boyce and Bobby Hart, Come on Down to My Boat, Hang on Sloopy. And at the other end of the decade, "Hair," Blood Sweat and Tears.
That decade covers my formative years, from 5 to 15 years old. Amazing how the music triggers (MANY!!!!!) certain memories. Monkees, Homer and Jethro.
I Want You Back - 1969 Jackson 5
I Want You Back - KT Tunstall 2005 (start around 1:40)