They have been named locally as Nathan Corrigan, Peter Finnegan and Peter McNamee.
The crash happened on the A5 Omagh Road in Garvaghy at about 1.50 am.
Police said the men, who were all in their 20s, were pronounced dead at the scene of the crash.
A fourth man, also in his 20s, was taken to hospital for treatment to serious injuries.
The three men who died and the man who was injured were in the car.
The driver of the lorry was not hurt, police said.
On its Facebook page, Clogher Eire Ogs club said it had received communication from the Finnegan family following the crash.
“Patrick Sr, Catherine, Patrick, Sarah, Daly, Elizabeth and the entire Finnegan and Daly families, at the untimely and tragic death of their beloved son and brother Peter, appreciate all your kind prayers and thoughts.
“We would request that the house is private, only for family and close friends,” it said.
All three men who died were from the local area.
Parish priest in Beragh, Monsignor Colum Curry, was at the scene of the accident on Monday.
“It was a horrific accident – a lot of debris scattered over the road, the car was on its roof,” he told Good Morning Ulster.
“The whole event just reminded me that life is precious and very fragile.”
Monsignor Curry said there was little people could say to the the bereaved families
“There are very few words that I think can adequately speak into such terrible anguish,” he said.
“I suppose the best we can do is just try to be present and help them in some small way just to cope with the darkness of this awful event.
“It has just been a huge sock to everybody.”
Police have appealed for anyone with information about the incident to contact them.
Deputy First Minister Michelle O’Neill tweeted that the news of the deaths of three young men was “heartbreaking”, adding that her “thoughts and prayers” were with the families and their friends.SDLP MLA for the area, Daniel McCrossan, said he had concerns about the safety of the A5 road.
“I heard the news this morning and I was very, very was concerned about the profound impact this will undoubtedly have on each and every person that knows those young lads,” he said.
“It is an extremely dangerous, extremely difficult road for people to travel on and it’s absolutely essential for people to travel on because they have no alternative.”
The Omagh Road had been closed while crash investigators examined the scene but it has since reopened.Tags: