Openside flanker Regan Tamihere has also decided to leave the province although the team has plenty of cover in the loose forward department.
With Kees Meeuws retiring, the only prop Otago has on its books is new signing Jacob Ellison.
Aulika moved to Dunedin in late 2010 and made an instant impact, ending the season as Otago's top try-scorer, although the province had a poor record that year, finishing last in the ITM Cup.
Aulika (28) was then picked for the Highlanders last season but made just one appearance off the bench and was not selected for the squad this season.
He had a limited time in the Otago jersey last season, playing for Tonga at the World Cup.
McGougan (27) was a late signing for Otago last year and played only a handful of games as he was dogged by injury problems.
Aulika is believed to have gone overseas after not being selected by the Highlanders while McGougan has returned to Bay of Plenty.
Scott Manson, who played a few games at prop for Otago last year, has not yet been signed by the union this season. Former Otago prop Ben Nolan, who did not play for the side last year, has gone overseas to play.
Tamihere (27) was signed last year by Otago and took a leave of absence from the police force.
However, he is returning to the police force in Auckland and his contract with Otago has ended.
Union chairman Wayne Graham said no new signings had been made in the past few weeks since Otago named its 2012 squad in November.
The squad did not contain a halfback and only one hooker but Graham said one or two players were floating around and may be contracted.
Otago coach Tony Brown is due to arrive in Dunedin late next month after coaching in Japan.
