When I first saw this thread I assumed that "Orange Songs" was in reference to songs of protestant Northern Ireland. Apparently many others did, too. There are some good songs. The Old Orange Flute and The Orange and the Green are two that Reiver 1 and I used to sing, in addition to the Ballad of William Bloat that I posted on this thread some time ago.
My best memory of those days was when we were asked to provide music for a gathering of the Orange Lodge Ladies Auxiliary of British Columbia, that was being held in Kamloops, B.C. where we lived. [I'm not sure if that was the exact name, but it was something like that.] After carefully screening out all the IRA songs or any that we thought might offend the good ladies, we sang other Irish songs for probably 45 minutes, which they seemed to enjoy. Then for our final number, we sang a verse or two of "Lord Nelson" which begins, "Lord Nelson stood in pompous state upon his pillar high. And down along O'Connell Street he cast a wicked eye." It goes on to relate how the IRA blew up the statue in 1966. The Orange ladies grew very quiet, and many smiles had turned to frowns, when we launched into "The Sash My Father Wore", a kind of Orange anthem that is set to the same tune. By the time we finished the first line the entire audience was smiling, clapping and singing with us.
Afterwards when we were putting away our guitars a number of ladies stopped to tell us how much they enjoyed the program. Finally, an elderly, dowager-type lady turned to me and asked where in Northern Ireland we were from! I said, in my best fake Irish accent, that we weren't actually from anywhere in Ireland, that Reiver 1 was a Liverpudlian and I was a Yank. She gave me a long puzzled look, then suddenly broke into a broad grin and said, "Och, go on wi' ye! Y'ur pullin' me leg! I can tell you're both from Belfast!" With that she turned and left, and I heaved a great sigh of relief.