Ask Meg Dwyer where she’s from, and you’ll get a complicated answer. “That's the hardest question, so we'll get it out of the way,” the Sweet Magnolia saxophonist and songwriter says carefully one Saturday morning in April. “I'm not really from anywhere, to be honest.”

She’s not. Her father was from England, and her mother was from Houston, but Dwyer’s grandmother has ties to New Orleans. After living abroad in the Middle East and Asia, Dwyer’s family finally moved back to Houston, where s...