I hope you are taking your cat to the vet. A rabies booster must be given to any pet who receives a bite of unknown origin.
Bite wounds are so serious because the bacteria from the mouth is delivered by the teeth directly into blood circulation, therefore, there is the potential for septicemia (blood infection), which can be life threatening.
He needs to be taken to the vet today! You didn't say how large the wound is (cm?) but if you can see muscle, the wound needs cleaning and possible stitches. The chest wound sounds even more serious. The doctor will clean the areas, stitch/staple what needs to be done and give the cat antibiotics. The horrible smell is probably infection which can be deadly if it goes systemic.
If the cat was in a fight with a wild animal, like a raccoon, then there are other illnesses to be considered and only a vet can help you there.