Vincent opened the scoring for Colchester on 24 minutes with a goal from close range after Swindon failed to the ball away.
Swindon equalised just before half time after breaking away after a Colchester corner. Ben Hutchinson made a long run before passing to Odabeyi who scored his second goal of the season to make it 1-1.
The best chance of the second half fell to Alex Revell who hit the bar with a 40 yard strike.
Overall a good game, where a draw was a fair result with both sides having plenty of chances. Phil Smith had a few saves to make to keep the score down. The draw moves Swindon up one place to 5th going into Saturday's away trip to Walsall.