AUSTIN, Tex. — In the five years since Noah Pozner was killed at Sandy Hook Elementary School in Newtown, Conn., death threats and online harassment have forced his parents, Veronique De La Rosa and Leonard Pozner, to relocate seven times. They now live in a high-security community hundreds of miles from where their 6-year-old is buried.

“I would love to go see my son’s grave and I don’t get to do that, but we made the right decision,” Ms. De La Rosa said in a recent interview. Each time they have moved, online fabulists stalking the family have published their whereabouts.

“With the speed of light,” she said. “They have their own community, and they have the ear of some very powerful people.”

On Wednesday in an Austin courtroom, the struggle of the Sandy Hook families to hold to account Alex Jones, a powerful leader of this online community, will reach a crossroads. Lawyers for Noah Pozner’s parents will seek to convince a Texas judge that they — and by extension the families of eight other victims in the 2012 shooting that killed 20 first graders and six adults — have a valid defamation claim against Mr. Jones, whose Austin-based Infowars media operation spread false claims that the shooting was an elaborate hoax.

The Pozner hearing is a bellwether in three cases, including another in Texas and one in Connecticut, filed by relatives of nine Sandy Hook victims. It comes as the social media platforms Mr. Jones relies upon to spread incendiary claims initiate efforts to curb him.

The day after the Pozner case, in the same courthouse, is a hearing in a separate defamation case against Mr. Jones brought by Marcel Fontaine, who was falsely identified on Infowars’ website as the gunman in the Parkland, Fla., school shooting in February. Mr. Fontaine, who lives in Massachusetts, has never visited Florida. The Pozner family and Mr. Fontaine are being represented by Mark Bankston of Farrar & Ball, a law firm based in Houston.