It was the second game for the Harambee Stars’ full-back since he made his international debut against Zambia
Simoes Inacio scored for Oduor’s side in the 18th minute before Stoke City equalised in the 44th minute via Tykes Campbell’s strike.
Hard-fighting Barnsley regained their lead in the first minute of added time of the first half through Dominik Frieser but the hosts equalised again in the 48th minute courtesy of Tommy Smith.
Stoke City would have won the game had they made use of the many chances they created in the final stages of the game even after they were reduced to 10 men after Nathan Collins was red-carded.
Oduor and his teammates are now sitting in the 21st position with three points while Stoke City moved to 10th place.
Barnsley’s caretaker manager Adam Murray said he is frustrated his players failed to pick up a win.
“Unbelievable frustration that we’ve not come away with a win, if you come to a place like Stoke in the Championship and score two goals away from home you expect to be winning the game,” Murray told BBC Sports.
“I’m really disappointed that a mistake’s played a big part in the game, but it’s something that we have to let go, [Walton] Jack’s been outstanding since we came back from lockdown and probably kept us in the league.
“We’re creating a lot of very good opportunities, we’ve spoken to the boys a lot over the last few weeks about getting into certain areas and getting into the assist zones to make chances, better chances, and we did that tonight but we’re missing that ruthlessness and that killer touch.”
On his part, Stoke City’s Michael O’Neill blamed the assistant referee for the outcome and the red card given to Collins.
“I thought the assistant was poor all night and the decision he gave, how he gives it, it was so instant, we could hear him shouting ‘red card, red card’ straight away,” O’Neill said.
“And having watched it back Nathan’s just blocked the striker’s run as you’d expect a centre-back to do and the Barnsley player’s thrown himself to the ground and held his face.
“It’s not really the referee’s fault as the referee has to take the information that he’s given by the assistant, but having watched it back the assistant should never have been making that decision.
“I’m not sure he’s in a great position – he’s looking along the line but there are three bodies between him and Nathan as well.”
Stoke City came into the match unbeaten and were lucky to avoid one in the hands of managerless Barnsley.