The day after Thanksgiving, Susan and Lorelai Woodruff saw approximately 10 brightly lit objects banking and turning quickly in the night sky above their home in Elsinboro, in southern New Jersey.

Every night since, they say, the objects have been back, emitting a strange, humming whir and flashing red, green and white.

“I think it’s like an invasion,” said Lorelai Woodruff, 52. “I feel like our privacy is kind of invaded.”

A month after reports of mysterious flying objects began spreading across the state, investigations by federal, state and local agencies into what they are and where they are coming from are ongoing. Many residents, like the Woodruffs, believe the objects are drones and have been left frustrated and perplexed at the lack of answers from authorities.

Emily Ferguson, 49, said a rash of sightings near her home in Mendham, in northern New Jersey, had been the talk of the town, and that her three children had started asking questions about them that she could not answer.

“The kids are all asking, ‘What’s going on?’ and ‘Why do we have to close all of our blinds?’ which is something we never do,” Ms. Ferguson said.