ELGIN, Texas—One person was killed and more than a dozen were injured when tornadoes tore through parts of Texas and Oklahoma, damaging a school, homes, and businesses, officials said. The same storm system was poised to move into Louisiana and Mississippi on Tuesday, carrying the risk of dangerous tornadoes and powerful winds. In Texas, several tornadoes were reported Monday along the Interstate 35 corridor, particularly in the Austin suburbs of Round Rock and Elgin, and close to Dallas-Fort Worth. Two unconfirmed tornadoes caused damage in the Lake Texoma area of northern Texas and southern Oklahoma. In Elgin, broken trees lined the rural roads and pieces of metal—uprooted by strong winds hung from the branches. Residents stepped carefully to avoid downed power lines as they worked to clean the remnants of broken ceilings, torn down walls and damaged cars. J.D. Harkins, 59, said he saw one tornado pass by his Elgin …