The speaker performed the swearing-in during the House proceedings in Lafia, Nasarawa State capital, on Monday.
Judge Jeffrey Gilbert strongly advised lawyers on both sides of the matter to appear in court for a hearing on Tuesday ahead of an imminent ruling during the week.
As early as 7:30 a.m., lawyers and journalists were checked by security operatives.
Mr Obi, a former governor of Anambra, turns 62 on Wednesday.
The APC held that Messrs Abubakar and Obi only dumped documents on the court, hoping they were enough evidence to strip Mr Tinubu of his presidency.
