Obadeyi hit home in first-half injury time to cancel out Ashley Vincent's 21st-minute opener.
It looked as though Colchester were better equipped to win the game as they opened strongly with quick, precise passing.
They were rewarded when Vincent lifted the ball over Phil Smith in the Swindon goal, only to be injured in the process and then stretchered off. Vincent's strike sparked Swindon into life, although it was not until the game ticked into first-half added time that they got their breakthrough.
Swindon broke from the edge of their own area, then Ben Hutchinson delayed his pass just long enough for Obadeyi to pick his spot before rifling an unstoppable shot into the net.
A brilliant 30-yard shot from on-loan Alex Revell which cannoned off the Colchester bar was Swindon's best second-half effort and even the introduction of top-scorer Billy Paynter could break down the U's defence as both sides settled for a point.