As eclectic as the New Orleans music scene is, it’s still hard to imagine an artist having a more diverse career than Anjelika “Jelly” Joseph, who, at the age of 31, sings in three bands that could hardly be more different.

Until recently, she was primarily known for her role as the backing vocalist and self-described “hype-man” for the wildly eclectic Tank and The Bangas, who are one of the five nominees for this year’s Best New Artist Grammy (see cover story). But now, Joseph is also com...