The House itself is a crappy dump with very little room. The boys are forced to share abed room and there is no air conditioning. Lois and Hal moved into the house while she was pregnant with Malcolm. They were unable to pay the rent for the apartment they used to live in, and so they unwillingly went to a crummy old house that was a lot cheaper.
Ever since they moved into the house, all of their children were born on the house's property. Malcolm was born on the front lawn, Dewey was born in the backyard, and Jamie was born in the guest bedroom. (Flashback, Baby Part 2)
Francis lived in the house until sometime in the year of either 1999 or 2000, where he was sent to military school for doing a stream of unbelievably terrible events. The final straw was getting his nose pierced. Although he never actually went back to living in the house again, he did come back to visit multiple times.
Craig Feldspar has lived in the house with them for a short period of time. In the episode Malcolm vs. Reese, The Wilkerson family burned down Craig's house and he went to live with them, while it was being rebuilt. He tortured the family the entire time by making a bunch of unreasonable requests and then guilt-tripping them into feeling obligated to do it, by mentioning that they burned down his house. This went on until the episode Mini-Bike, where Reese broke his leg on a mini-bike and then tricked Craig into thinking that he did it, by laying down behind his car as he was backing it up. When Craig saw that he did this, he felt overlaid with guilt and left the house to go and live somewhere else.
In the episode Graduation, Malcolm and Reese graduated high school and went to live on their owns. Malcolm lived in the college apartment and Reese lived in Craig's house with him.