Getting rid of mice and rats

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Ever since our cat died the mice have invaded the house. We set up traps, put poison and coverd all the holes but we still would see them running around. We moved our food up higer so they wouldn't have anything to eat. They learned how to get on the table and inside the stove. For the past few nights I heard banding in the walls that confused me then tonight I noticed three rats running around. I know there comeing from outside. We could put traps out but that wont even make a dent. Kill four and six more will come in from outside. Also we don't want the dogs noses snaped with the rat traps. I don't know what to do anymore. Help please?