Sounds like a Tom and Jerry cartoon!
1. Thoroughly clean toilet.
2. Lift both lids and add shampoo.
3. Find and soothe cat as you carry him to bathroom.
4. In one swift move, place cat in toilet, close both lids and stand on top, so cat cannot escape.
5. The cat will self agitate and produce ample suds. (Ignore ruckus from inside toilet, cat is enjoying this.)
6. Flush toilet 3 or 4 times. This provides power rinse, which is quite effective.
7. Have someone open outside door, stand as far from toilet as possible and quickly lift both lids.
8. Clean cat will rocket out of the toilet and outdoors, where he will air dry.