The tune is identified as an "Irish Reel" in Kerr's Merry Melodies vol. 1 (c. 1880's), although it is a polka and not a reel. It appears under the probably American title "Oyster River" set as a hornpipe in William Bradbury Ryan's Ryan's Mammoth Collection (1883), perhaps referring to Oyster River, New Hampshire. The hamlet of Oyster River Plantation was the scene of a devastating massacre during King William's War in 1694. Abenaki Indians, incensed at abuses from the English population and encouraged by the French, killed and captured nearly 100 settlers, one third of the population.
I learned the first two parts of this at our Monday night jam.
The reason for the octave double stops in the B part is that if I am playing this on tenor banjo or octave mandolin I like to slip into the lower octave occasionally. I sometimes do that on mandolin or fiddle just for fun. I don't play both notes simultaneously.
I learned the third part from Adam Hurt and Megan Lynch Chowning's CD Inside Out. If you play the C part, play AA BB CC and end with either an A part (omit the pickup to B) or a B part.