Occidental Petroleum Corp., the largest oil producer in the giant Permian Basin, has ceded to activist investor Carl Icahn’s demands and announced deep spending cuts in a bid to survive the steepest crude-price plunge in decades. The truce with Mr. Icahn, unveiled Wednesday, is the culmination of a monthslong battle that began last year after Occidental outbid Chevron Corp. for Anadarko Petroleum Corp. Two…