A proper onager wouldn’t have had wheels. This is because when the arm was released, the power put through to the projectile was so much that the onager would buck and jump. If there had been wheels on the onager, the whole catapult would roll backwards violently and leave the projectile sitting not very far away. Imagine a fool standing on a skateboard and throwing a bowling ball forwards. What’s going to happen? The skateboard will roll backwards and the fool will likely fall off. The bowling ball will not go very far and may even end up landing on the person who threw it. Since the goal was to get as heavy a projectile as possible to travel as far as possible, it would have been foolish to put wheels on the onager, even on a small one.
Also, an onager used as a siege-engine for destroying walls would have been so large that wheels would have been impractical. It would have been too heavy to move and the wheels would have gotten stuck in the ground. The half-sized catapult that Sir Payne-Gallwey made was two tons so a full sized one would have been twice that. Such large onagers would have been built or at least assembled on site. When large onager’s were made, special areas designed to soak up the compression would have to be created or it would buck and destroy the ground under it, causing it to lose it’s aim.