WILLISTON, N.D.—With the nearby oil boom draining this city of many of its service workers, businesses here are relying on a cultural-exchange program for foreign college students to keep the local economy humming. More than 500 foreign students—from Thailand, Jamaica and about a dozen other countries—are staffing nearly every hotel, car wash and fast-food place in town, tending to the troops of roughnecks from the oilfields. "Without them, I don't know what we'd do," said Ward Koeser, mayor of this city of 16,000, citing long lines, slow service and limited hours at stores and restaurants before the students arrived. But...