Now, for the first time, the families are confronting Mr. Jones in court.

“When anybody’s behind a machine, whether it’s a gun or a computer or a car, a dehumanization takes place that makes it easier to commit an act of violence,” Veronique De La Rosa, the mother of Noah Pozner, another victim, said in an interview. She is suing Mr. Jones, she said, because she wants to force him to admit to his devotees that “he peddled a falsehood, that Sandy Hook is real and that Noah was a real, living, breathing little boy who deserved to live out the rest of his life.”

In three separate lawsuits — the most recent was filed on Wednesday in Superior Court in Bridgeport, Conn. — the families of eight Sandy Hook victims as well as an F.B.I. agent who responded to the shooting seek damages for defamation. The families allege in one suit, filed by Koskoff, Koskoff & Bieder in Bridgeport, that Mr. Jones and his colleagues “persistently perpetuated a monstrous, unspeakable lie: that the Sandy Hook shooting was staged, and that the families who lost loved ones that day are actors who faked their relatives’ deaths.”

More broadly, the families are seeking society’s verdict on “post truth” culture in which widely disseminated lies damage lives and destroy reputations, yet those who spread them are seldom held accountable. The suit filed on Wednesday emphasizes Mr. Jones’s reach and connection to Mr. Trump. On his show last year, Mr. Jones called himself and his listeners “the operating system of Trump.” Later he said, “I’m making it safe for everybody else to speak out just like Trump’s doing, on a much bigger scale.”

When the president called the news media the “enemy of the people” last year, Mr. Jones proudly tweeted that he used the phrase first, in 2015.

Mr. Trump has also echoed InfoWars’ false claims that Hillary Clinton benefited from the votes of millions of illegal immigrants in the election, and repeated InfoWars’ bogus charge that the news media covers up terrorist attacks.

Fantastical explanations for traumatic events punctuate history. But 21st-century conspiracy theorists gather in vast online networks where bogus claims reach millions in minutes, and where participants like Mr. Jones use social media and online marketing to turn an eccentric preoccupation into a thriving commercial enterprise.

Mr. Jones pitches the false claims, along with diet supplements and survivalist gear, on his InfoWars website, radio program and YouTube channel. His videos have been viewed more than a billion times. He most likely sells $7 million to $12 million worth of diet supplements a year, according to an analysis in New York magazine.

Sandy Hook families have been followed, videotaped and harassed by people demanding “proof” that their loved ones died. Monuments to the slain children in Newtown have been stolen and defaced. An Alex Jones devotee went to prison last year after phoning and emailing Leonard Pozner, Noah’s father, with death threats, including “LOOK BEHIND YOU IT IS DEATH.” The family relocated to a gated community with 24-hour security. Their daughters, who survived the shooting, check doors and windows before going to bed, and sleep with the lights on.

Nate Wheeler, 15, who hid in a school supply closet during the shooting that killed his 6-year-old brother, Ben, struggles to understand false online claims that both boys and their parents were “crisis actors” and that his brother never died, his father, David Wheeler, said in an interview. Mr. Wheeler has found messages on his social media accounts telling him that he will face divine judgment for lying when he dies, he said.

Wednesday’s suit follows twin defamation lawsuits filed in Texas in April by the parents of two other victims — Mr. Heslin, and Ms. De La Rosa and Mr. Pozner. Mr. Jones did not respond to requests for comment. After the Texas lawsuits were filed last month, he posted a 10-minute videotaped response suggestive of how his positions on the event shifted. “I questioned the P.R. and the talking points that surrounded the Sandy Hook massacre,” he said. “But very quickly I began to believe that the massacre happened, despite the fact that the public doubted it.”

And yet in an earlier video on his website, titled “Alex Jones Final Statement on Sandy Hook,” he says: “If children were lost in Sandy Hook, my heart goes out to each and every one of those parents, and the people that say they’re parents that I see on the news. The only problem is, I’ve watched a lot of soap operas, and I’ve seen actors before.”