It isn’t just that there is too much oil sloshing around the world. All of a sudden, there are fears of too little demand for the stuff too.

Oil prices continued to tumble Thursday, with Brent crude, the international benchmark, falling 5% to its lowest levels in more than a year. The U.S. benchmark, West Texas Intermediate, settled at $45.88 a barrel, a 17-month low, and is down 40% since a high in October.

The...