Rossco Stern, 23, Charlie Hill, 33, and Gary Thoms, also 33, carried out the attack after turning up uninvited to the Halloween party in Dundee.
Sheriff George Way described the three men as "feral thugs".
Stern and Hill both admitted the charges and Thoms was found guilty by a jury following a trial.
Stern and Hill were each jailed for three years and two months, while Thoms was sentenced to three years and four months in prison.
A trial at Dundee Sheriff Court heard that the men were thrown out of the party on 1 November 2015 after sparking an argument.
CCTV footage showed victims Liam Holt, Fraser Nicoll and Michael Craib being attacked as they tried to flee the attackers.
Mr Holt was seen being thrown to the ground before one of the gang repeatedly struck him on the head with a baseball bat while another, identified as Thoms, kicked his head.
Knives were seen being brandished and repeatedly used on the victims, who eventually escaped.
Stern, from Glasgow, and Hill, from Dundee, each admitted two charges of assault to severe injury and permanent disfigurement.
Thoms, 33, from Dundee, was found guilty of assaulting Liam Holt to his severe injury and permanent disfigurement.
Kevin McCarron, defending Stern said: "He fully accepts custody is merited and he acknowledges the consequences could have been far more serious.
Solicitor advocate Jim Laverty, for Hill, said: "He is utterly ashamed of himself and utterly ashamed of watching the CCTV."
Mike Short, defending Thoms, said his client realised there was no excuse for his behaviour but insisted the death of his father had an impact on him as well as terminal cancer suffered by his grandfather.
All three will be supervised for a year in the community following their release.
Sheriff Way said: "The attack I saw on CCTV footage was absolutely atrocious.
"They were being pursued by you like a pack of vicious dogs.
"They were no threat to you or any of your friends."
Three men who attacked a man dressed as Dracula and his two costumed friends with knives and a baseball bat, have been jailed.