So... is Yagami-kun no Katei no Jijou finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: May 25, 1990
Manga finished: May 01, 1990
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Yagami-kun's home life is...complicated. His mother looks incredibly young, and he harbors some rather inappropriate feelings towards her.
This situation is further complicated by his teacher, who is also infatuated with Yagami-kun's mother, leading to a bizarre rivalry.
Meanwhile, his father is not without his own admirers, specifically his secretary. However, she has a change of heart upon learning about his wife.
This leads to a tangled web of affections and rivalries, with Yagami-kun caught in the middle, struggling between his feelings for his mother and the attentions of a new girlfriend.