Joseph Cascella, 54, owner of the Prego Delly on Capitol Hill and a former national representative of the American Federation of Teachers, died Monday at Capitol Hill Hospital.He had a liver ailment.

Mr. Cascella moved to Washington in 1977 and opened the Prego, which specialized in Italian delicacies. He operated the business until his death.

A native of Newark, N.J., Mr. Cascella served in the Navy in the Pacific during the World War II. After the war, he earned a degree at Montclair (N.J.) State Teachers College and became a teacher of social studies in the Newark public school system. He also became active in the American Federation of Teachers (AFL-CIO) and an officer of its local in Newark.

In 1965, he was hired by the AFT as a national representative. He lived in Belleville, N.J., until he was transferred to Phoenix, Ariz. He resigned from the union in 1977 and moved to Washington.

Survivors include his mother, Delia Cascella of Newark; two sisters, Marion Knight of Belleville, and Dolores Cascella of Newark, and three brothers, Nick and Victor, both of Newark, and John, of Branchberg, N.J.

The family suggests that expressions of sympathy be in the form of contributions to the Children's Hospital National Medical Center, Washington.