Kriza danced with ABT from 1940 to 1966. He originated rôles in ballets by nearly every major choreographer from the period, including George Balanchine, Agnes de Mille, Eugene Loring, Léonide Massine, Jerome Robbins, and Antony Tudor. Some of the most significant include one of the sailors in Robbins' Fancy Free (1944) and the Pastor in de Mille's Fall River Legend (1948); he is probably best-remembered, though, for his performance in the title rôle of Loring's Billy the Kid. Kriza's regular partners included Nora Kaye and Ruth Ann Koesun.
Although Kriza did not appear in Hollywood musicals, he performed regularly on television—most significantly in the title rôle of Billy the Kid for Omnibus (1953). Other credits include the Pastor in Fall River Legend and the Champion Roper in Rodeo, also for Omnibus. A number of archival films exist at the New York Public Library.
Kriza was the brother of Lillian Rosicky and George J. Kriza, son of John Kriza and Marie Kriza. His nephews included Ed and George Rosicky and George L. Kriza. He lived in Bloomingdale on his parents' farm. He was well known in Berwyn where he grew up, attending Morton High School. He was often featured in the local Berwyn Life, and was well known among his community for his ballet achievements. In the course of his career, he danced for John Kennedy in the White House, Khruschev in the Kremlin and before other dignitaries. He was a member of the original cast of American Ballet Theatre.