In English translation, there are two Greek words translated to the single English word, oikia and oikos. They are from the same root, but one is the female form of the word and the other the masculine. They have very similar meanings though oikos is broader than oikia.
Typically, Jesus uses different words to mean different, even if slightly different, things. Jesus may use them interchangeably, but I haven't made a close enough analysis of his use to decide for sure. It seems like the different evangelists use these two different terms in similar verses, further clouding their differences.
"House" as oikia, means "house", "building," and "household." It refers to the building itself, all the people that dwell in it, including slaves and servants, all property owned by that family, and all the descendants of the continued line. We might say "estate" in English to capture this idea moe clearly.
"House" as oikos, which means "house", "dwelling place", "room", "home", "meeting hall", "household goods", "substance," and "ruling family." It is any dwelling place but not exclusively a separate house. It is any dwelling place but not exclusively a separate house. It means the household or clan that lives in the building as well. which means "house", "building," and "household."
Several other Greek terms, translated in various ways, are based on this concept of a "house." "Goodman of the house" is from a compound Greek, οἰκοδεσπότης, word that is literally the "master of the house." It was translated as "householder." The verb often translated generically as "build" is a word that specifically means "build a house," oikodomeo, though it generally, "build", "fashion," and so on.
Lest we forget, but Jesus and his earthly father Joseph were house-builders so the idea of a "house" had a rich symbolism for him. (The Greek term describing Christ and translated as "carpenter" is actually closer in meaning to "mason" and refers specifically to someone who builds houses as opposed to working with wood, for example, building furniture.)
As a house builder, Jesus uses the terms "house" in both its meanings. He uses it to as a structure whose architecture matters. His first major parable using the idea of a house deals with building it on a solid foundation (Matthew 7:24). For him, a house that cannot stand is in a very physical sense, no house at all.
Second, he sees a "house" as a family or a clan, encompassing all the people in the house and headed by the master of the house. For Christ, the world of men is divided into kingdoms and kingdoms are divided into houses (Matthew 24:43). Belonging to a given "house" is a matter of personal allegiance (Matthew 19:29) to the master. The house can be judged as a group (Matthew 10:13). The role of the master of the house is to protect the people and property within the house. (Matthew 12:29, Matthew 24:43).
In Mark 3:25, Jesus says that a house divided against itself cannot stand. On one level, this verse is a simple logical statement about what makes up a house. A divided house where there is a clear split between its members become two houses. Think of a clan where one branch of the clan separates itself from the others.
A member of a house cannot be against the master of his house because his membership in a house depends on his allegiance to the master. Nor can a master of a house be against his (or her, widow's also have houses Matthew 23:14) house's members because his authority comes from the responsibility of protecting those members from outsiders. The violation in either half of this contact, the lea - der's or a follower's, destroys the house itself as a unit.