Why did the house continue to serve food and clean up after itself ?

The house continues to serve food and clean up after itself because it is nothing more than a mechanical object that has been programmed to behave in this way. It has no way of knowing that the family that it feeds and serves has been obliterated in a nuclear holocaust. It is simply a machine.
The point of the house going on with its now meaningless activities of making breakfast, cleaning, and setting up a card table for bridge is to show how technology is divorced from the natural world. The house has no soul and no real feeling for the people it serves, although it has been programmed to sound humane and caring.
Through this story, Bradbury hopes to alert humankind to the need to control technology before it ends up destroying us.