The duo started their careers with Tottenham, and played together last season with Hayes & Yeading United.
McNamara, who has also handed trials to former St Mirren defender Graham Carey and Turkish winger Nadir Ciftci, welcomed his players back for the beginning of pre-season training at their base in St Andrews on Monday.
"There are a lot of things still happening player-wise and hopefully by the end of this week we will have the right ones in," McNamara said.
"There are two lads here who have been with Spurs - Butcher and Oyenuga. I've watched them in a trial game.
"Both impressed us so we have moved to bring them here. Butcher is a centre-half and Oyenuga is a forward."
The Tannadice club have also taken former Norwich goalkeeper Lee Camp on trial after his departure from Carrow Road this summer.