Looks like 337th ECB is the unit you've been looking for. Originally 3d Battalion, 213th Coast Artillery (Antiaircraft) of the Pennsylvania National Guard, the battalion was activated at Allentown, Pennsylvania in September 1940.
The entire regiment landed at Casablanca, French Morocco, ten days after the Invasion of North Africa. The regiment was broken up 1 April 1944 and its former elements were reorganized and redesignated, 3d Battalion becoming 337th Antiaircraft Artillery (Searchlight) Battalion. Eight months later, 337th AAA Battalion was, in turn, reorganized and redesignated 337th Engineer (Combat) Battalion.
The battalion left Italy by increments in mid- to late July 1945, was reunited on Luzon, Philippines the following month and was involved in repairing war damage in and around Manila until inactivated in 1946.
The battalion served in North Africa (Algeria-French Morocco & Tunisia Campaigns), Italy (Naples-Foggia, Rome-Arno, North Apennines & Po Vally Campaigns) and the Philippines. Campaign credits to which your Dad would be entitled would depend on when and where he joined the battalion and this would require a review of official records.