Private-equity funds that once profited from energy deals in North American shale are hunting in a new bargain basement for cut-price oil-and-gas fields: almost everywhere else. Flush with cash from recent fundraising, the groups are looking for assets with owners who have been hurt by the precipitous fall in oil prices—from the North Sea to Nigeria, South America to Southeast Asia. Their previous success in North America—where unconventional oil drilling has led to a boom—has stoked demand from investors, such as pension funds, endowments and insurance companies.