Oxtoby made four changes to the side that started on Friday as Nadene Caldwell, Caragh Hamilton, Halliday and Weir were all handed starts.
Despite the hosts dominating possession early on, Romania went close to scoring on five minutes.
Maria Ficzay's free-kick deflected off Halliday and fell kindly into the path of Ana Maria Stanciu, who was unable to direct her header on target.
Northern Ireland then went ahead after a well-worked move involving two of the young players brought into the starting team.
Brenna McPartlan released Halliday down the right and she squared the ball for Weir to sweep home from six yards.
Oxtoby's side continued to look dangerous every time they went forward but, like on Friday, they lacked the cutting edge in the final third to add to their advantage.
Their sloppiness in possession allowed Romania back into the game and they nearly equalised three minutes before half-time.
Ficzay floated in a free-kick which Jackie Burns could only punch out to Florentina Olar-Spanu and her fierce strike was cleared off the line by Ellie Mason.
Burns then turned Olar-Spanu's looping effort over the crossbar after Stefania Vatafu found Romania's captain unmarked on the edge of the box, as NI were forced to dig deep to hold on to their lead heading into the break.