Two teens aged 17 and 19, who are from the Omagh area, were detained on Thursday, while an 18-year-old man was arrested in the town on Wednesday.
Meanwhile, a 21-year-old man has been released on police bail pending further inquiries.
Jason McGovern, 19, was found dead in bed at about midday on New Year's Eve - after being seriously assaulted in the early hours of that morning.
The victim had made it back to a friend's house in Emyvale, Co Monaghan, having been first attacked by a group of about five youths outside the Terrace Bar at John Street in Omagh.
When he was followed by at least three of the original group, Jason was again attacked as he tried to get a taxi outside the Weigh Inn at Kevlin Road.
He was struck so hard that he was knocked to the ground and officers believe that may have been the blow that killed him. A post-mortem examination has shown that he died from head injuries.
On Wednesday, the detective leading the murder investigation appealed for witnesses or those involved to come forward.
"I need to establish what took place and what was said between the assailants and the victim," Detective Chief Inspector Richard Harkness said.
"There are two sides to every story. I want to establish the facts."