Stockdale has returned for a second loan spell with the Tigers but has not been given permission to play by parent club Fulham, while Oxley, on loan from Burton, has already appeared for the npower League Two side in the competition.
Swiss goalkeeper Eldin Jakupovic is therefore expected to return to the starting line-up.
Manager Steve Bruce has no new injury or suspension problems, but leading goalscorer Sone Aluko remains sidelined with a slight tear in his Achilles.
Forward Matty Fryatt (Achilles) and defender Joe Dudgeon (knee) remain long-term absentees.
Bruce made several changes to his line-up for the third round tie against Leyton Orient and could be tempted to rest some of his players against Barnsley.