I know humans used to have "Houses" comprised of people rather than structures, similar to the Klingon fashion. House of Mogh, House of John, etc. Is this house of people the house that needs to be put in order? What is the origin of the phrase, and what terms might I use to learn more about these houses?
“To put one’s house in order” is at least as old as the King James Bible. See this Wiktionary page https://en.m.wiktionary.org/wiki/put_one%27s_house_in_order.
The “house” can refer to one’s personal financial affairs, relationships with others, making a will, and the like.
From 2 Samuel 17:23, quoted in the Wiktionar article:
And when Ahithophel saw that his counsel was not followed, he saddled his ass, and arose, and gat him home to his house, to his city, and put his household in order, and hanged himself, and died, and was buried in the sepulchre of his father.
This page has a few more Biblical quotations that are similar: