The crash involving a car and a lorry happened at about 1.50am on Monday in the Omagh Road area of Garvaghy.
The parish priest in Beragh, Monsignor Colum Curry, said he visited the scene in the hours after the tragedy.
He told the BBC Good Morning Ulster programme: “It was a horrific accident – a lot of debris scattered over the road, the car was on its roof.
“The whole event just reminded me that life is precious and very fragile.
“There are very few words that I think can adequately speak into such terrible anguish.
“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 shock to everybody.”
The three men, all in their 20s, died at the scene.
A fourth man, also in his 20s, is in hospital and is being treated for serious injuries.
Deputy First Minister Michelle O’Neill tweeted: “Heartbreaking news that three young men have lost their lives in a fatal road collision in Garvaghy. My thoughts and prayers are with their families, friends and local community.”
Local SDLP MLA Daniel McCrossan called it “heartbreaking news”, adding: “My thoughts are with the families and friends of these young victims whose lives have been cut short in such tragic circumstances.”
Stephen Donnelly, a local Alliance Party councillor, said the incident was “devastating”.
“Three young lives lost and another seriously injured. Our thoughts as a community will be with all the families impacted,” he said.
West Tyrone MP Orfhlaith Begley said: “I wish to extend my deepest sympathy to the families of the three young men killed and the young man seriously injured.
“The scale of this tragedy has stunned the entire community, but everyone will rally around to support all those affected in what will be difficult days ahead.
“I wish to pay tribute to the emergency services for all their efforts at the scene.”