Zim's house was created by a small Irken device which created the building from Zim's rough sketch. Interestingly enough, from the opening sequence it appears that the only solid part of the house is the couch and the floor under the upper level (where the Voot Cruiser lands) and the walls are illusionary. Since the sketch was based on what Zim and GIR had observed as they flew over the town the house has some interesting decorations - including the yard gnomes, the flamingos, the "I heart Earth" sign and the mens room door.
The lawn gnomes are actually a defensive device - the gnomes have sensors and lasers built into them and they seek to destroy strangers who intrude upon Zim. The house is powered (and presumably attached to the phone system) by the large cables which penetrate the neighboring buildings.