My criteria for this subject is what songs are so good (in all or most of the five areas the OP mentions) that you cannot become tired of it, even if it was massively overplayed. The first few songs that immediately came to mind were:
Tired of Waiting - The Kinks
Nothing But a Heartache - The Flirtations
There She Goes - The La's
All I Want - Toad The Wet Sprocket
Tired of Waiting - The Kinks
Nothing But a Heartache - The Flirtations
There She Goes - The La's
All I Want - Toad The Wet Sprocket