The Real IRA exploded the car bomb in the market town on August 15, 1998, but despite extensive police investigations, no one was convicted of the crime.
The families' civil case, which is being heard at Belfast High Court, has so far cost an estimated $3.17m.
Bill Clinton, the former US president, who visited the town while in power, has been among the backers of the legal action, which has taken eight years to reach a verdict.
The families allege that Michael McKevitt, Liam Campbell, Colm Murphy, Seamus Daly and Seamus McKenna all played a role in the attack, which also left more than 200 people injured, a charge they all deny.
The court has heard from spouses, parents, brothers and sisters of the victims, as well as police officers who described the scenes of carnage they encountered at the scene of the bombing.
Daniel Brennan, the lead lawyer for the case, has said that if successful the judgement could open the floodgates for similar actions against fighters responsible for the bulk of the 3,700 deaths in Northern Ireland's four-decade conflict.
"Regardless of the result this has been worthwhile, it has empowered the families like never before," he said.