'Would it be misinterpreted if I suggested "Unpopular songs" – just to distinguish them from "Pop music" of course?'

Not sure that I'd be comfortable describing the non traditional songs I perform as 'unpopular songs' although some of our audience might ;)

But I take your point ST, If you look at publicity material we've used for the band it describes us as playing a mix of 'traditional, modern and original songs and tunes' although all grouped together under the term 'folk' and I've always been comfortable with that.

The term 'Acoustic' I've never been entirely comfortable with, it's a 'catch all' term and too loose, and could be any genre performed with acoustic instruments, but at risk of upsetting some, if I see an event billed as 'acoustic night' it immediately conjures up images of navel gazing singer songwriters for me.

John