Roaches can eat anything, even nonfood items like soap, paper, pet food, glue, garbage, etc. They like dark, moist places to hide in (like bathroom cabinets) so once they find a favorable environment with this (like your house) they move in and start to breed. They can get in from improperly closed doors, windows (faulty weather stripping) but a lot of times they are hitch hikers in boxes, paper bags, furniture. When they get inside the house they find cracks and crevices inside furniture and cabinets and walls so unless you bug bomb your house you will have a hard time getting rid of them completely. You can try hiring a professional exterminator and follow their regimen and professional recommendations. The cheap route would be of course to buy commercial bug sprays and do it yourself. Spray the baseboards and insides of cabinets, cracks around windows, etc. wherever you see them coming and going. If you don't like the smell of spray or are worried about its toxicity (animals and young children) you can try roach bait, or those "roach motels" which are passive adhesive traps with a bait scent inside. Diatomaceous earth is a very fine non-toxic powder or grit, that is used as a non chemical insecticide. These are good for those little German cockroaches that can be bug spray resistant. Keep your house clean and swept up. Take out the trash every time it gets full. Don't leave dirty dishes in the sink, or food out, even dog food, overnight. It is an ongoing process and battle, and I wish you the best of luck.
Greetings from Florida, home of the nuclear cockroach.