Food is one reason causing certain odors, and from the debris left in teeth, in mouth, being peutrified, but there are many other reasons, causes, illnesses, and then compounded by the radiation and chemo treatment causing mucocitus, ulceration, dry mouth, infections, increased plaque, and not being able to adhere to proper oral hygene, and necrosis of tissue, are some of the few.
Take care of what you can by seeing a dentist for teeth cleaning, plaque removal, treating dry mouth, brushing, flossing, rinsing after every meal, and there are a number of toothpastes, rinses that have some chemicals that help, the dentist may recommend. One is Chlorhexidine mouth washes.
I hope this helps.