My 10 year old sphynx cat twiggy has bad teeth. We adopted her at 8 and she has had 7-9 extractions since then. She only has 4 teeth left. Those too, may have to be removed as she gets abscesses near her remaining teeth. For now we are fighting the abscesses with antibiotics and a drug that helps her immune system. She has a brother Baci who is young and occasionally they play fight and nip at each other.....or I would have removed those last 4 teeth.
Like your cat, her breath was disgusting due to the rotten teeth. What happens in many cases is that rotten teeth produce gingivitis and other bad bacteria that enters the bloodstream and weakens the immune system. Gingivitis shortens the lifespans of both humans and cats.
In terms of food...my cat still eats kibble for breakfast and soft food for lunch and dinner.... I think eating soft food should cause your cat less pain than hard food if her teeth are really messed up...
I'd encourage you to go for a vet visit though (perhaps for antibiotics - pain meds)...tooth pain sucks for humans so it's got to suck for cats as well.