I assumed since he goes outside, that he might meet up with things like dogs and cars that could injure him. Being hit by a car could make him walk the way you describe, and breathe heavy. Cats can be injured internally, with no mark on the outside.
Good that his gums are pink in color.
The way I would go about finding out what is wrong with him would be to start with a good physical exam: Take his temp (normal rectal temperature is between 101 and 102), feel his pulses, palpate his internal organs and lymph nodes, listen to his heart and lungs with a stethoscope, try to determine if he is walking the way he is because of an orthopedic (bones, joints, muscles) problem or a neurologic (nerves, spinal cord) problem. Once I figure out what is wrong (fever, blood clot in the back legs, nerve problem) I know the best way to treat him.
If he won't eat or drink, he will become dehydrated. If this were my own cat, I would be trying to treat him at home; I would have him at my clinic for a good exam, and the exam would tell me what to do next (medication, Xrays , blood tests, fluids, etc.).
Let me know what other questions you have. Rebecca