The song Michi quoted reminds me of "Way Down in Shawneetown," by Dillon Bustin (although I am more familiar with the version recorded by Malcolm Dalglish and Grey Larsen). You can find more info in these threads:
Way down in Shawneetown
Shawnee Town
Way Down in Shawneetown - Dillon Bustin.

Although the shanties are obviously related, I'm afraid that "Shawneetown" doesn't shed any light on what "eye-corn" is. The corresponding line in "Shawneetown" is "We'll trade 'em down in Shawneetown and we'll bring the rock salt back."

The song that mentions tobacco is apparently a different song.