What are some reasons for really bad breath in a child with no teeth cavities?

Halitosis: Sinusitis, adenoiditis, foriegn body in nose and gerd would all be possibilities.

Oral hygiene: My first concern is a foreign body in the nose -- a rotting bean. Don't worry how it may have gotten there, kids are kids. Most bad breath in adults and children is due to decaying crud in the mouth, between the teeth or on the tongue. A good dental flossing with running it over the back of the tongue cures most of these. If it does not, look for a problem in the upper aerodigestive system.