Jukebox and Radio
Lots of these songs are from what we call Jukebox Musicals. Jukebox musicals are musicals that don’t have an original score. One well known example would Be Rock of Ages. Rock of ages has plenty of classic rock songs woven into a story line. This and Shows such as Grease and Smoky Joe’s Cafe also fit the bill.
There are Worse Things I could Do Grease
Want you Back by the Jackson 5
Anything from XANADU. (Roller skates not required.)