If you are running the right code (here is a link to the original VRC code by Cody ( Holonomic drives 2.0: A video tutorial by Cody) ) then you should be fine.
When you say the omni wheels get stuck, are the pins getting between the rollers and the wheel?
You show us the top view of the robot, but the bottom is important. Your wheel axles should be at the very bottom of the robot to make sure you have clearance past the pins.