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.