Obita initially joined Latics on January transfer deadline day and his emergency youth loan with the League One strugglers now runs until April 1.
The 19-year-old has made four starts and two substitute appearances in all competitions and opened the scoring in Oldham's 2-2 draw with Everton in the fifth round of the FA Cup at Boundary Park.
Meanwhile, fellow loanee Lee Barnard has resumed training following a hamstring scare.
The Southampton forward, who has scored twice in six games for Latics, missed Saturday's defeat to Sheffield United with the problem but was given the all-clear following a precautionary scan.
Another Oldham player on the mend is Cristian Montano. The winger is set for his first action since suffering a torn thigh muscle at Scunthorpe on New Year's Day in a Tuesday afternoon reserve match against Bury.
