I really would like some songs to fit those criteria.
We had a night here recently called "learning new songs". Everyone is pretty much fed up with the same dozen or so choruses that have been sung since age immemorial and so a night for learning new choruses was included in the program.
Only it was difficult to find new songs that are not complicated. Lyrics, tunes, rhythm, chords: all complicated.
Of the ten songs that were chosen, we learnt five. Some worked better than others. This was a few weeks ago now. It was a great night. They were good songs and we all really enjoyed singing them. And I think over time we'll learn them... especially as there is time set aside each week for practise.
But it got me thinking about songs we could sing without words and music (which we either can't read or can't carry around with us) which we could learn in one sitting. This would be great for teaching when students go into villages. Songs which could be passed on easily.