Ysvelia Silva planned to spend this spring training for the New York City Marathon. Instead, she is calling neighbors in her apartment complex and urging them not to pay rent next month.

She and other tenant organizers say the majority of residents at a group of 17 buildings in Queens, N.Y., have committed to a rent strike effective May 1. The neighborhood’s five-story brick buildings of mostly affordable housing belong to a larger complex called the Cosmopolitan Houses.

“Life...