Adams was being sued for “vindicatory” damages of £1 each by John Clark, Jonathan Ganesh and Barry Laycock, who were injured respectively in the Old Bailey attack in 1973, and the London Docklands and Manchester bombings in 1996.
The claimants raised more than £100,000 through crowdfunding to bring the case.
They said they were acting not just for themselves, but for all IRA victims.
The IRA was responsible for around 1,700 killings during the Troubles.
Adams was once charged with IRA membership in 1978, but the case was dropped due to insufficient evidence.
His only Troubles-era convictions, for twice attempting to escape prison while interned without trial in the mid-1970s, were quashed in 2020.
He has been questioned in court before about his alleged IRA past – at the Ballymurphy inquest in Belfast in 2019 and during a libel case against the BBC in Dublin last year.
