Fast-food workers, caregivers, adjunct professors, and janitors are among the workers in seven states planning to walk out of restaurants, hospitals, universities, and other establishments from Oct. 2 to Oct. 4 as part of a larger effort leading up to the midterm elections.

The plan is spearheaded by the Service Employees International Union-backed Fight for $15 campaign, which was established in 2012 to organize those in the fast-food industry and get better wages for them and other low-paid workers.

The...