Reverend mother Mohiam calls Alia an abomination when she first encounters her near the end of "Dune"¹. There is no indication in the story at that point that Alia is possessed or even under the influence of any of her forefathers at that point².
I read Mohiam's following statement "Long were we warned against such a one and how to prevent such a birth, ..." that the Bene Gesserit did, until then, never have to deal with such a child. The Fremen might have had to deal with such children before, but there is no clear indication in the books they do.
In "Children of Dune" The use of abomination is different: "Any possession reduced the possessed to Abomination."³
Also in "Children of Dune" the Duncan mentat Ghola reasons: "Therefore Alia was not in contact with that pseudo-Jessica within. Therefore Alia was completely possessed by another pseudo-life to the exclusion of all others. Possessed! Alien! Abomination!". You can interpret this as that "completely possessed" means all three of these, or that these are increasingly severe "states".
Alia herself uses Abomination as what the Bene Geserit call not resisting the "Great Temptation", prolonging life (without melange, if many Bene Geserit would do that it would be noticed).
In the book of Kreos (within a chapter header) "... the Sisterhood feared Alia, an adult Abomination, ..." which would imply there were non-adult Abominations as well, but Alia is not that. And Leto: "He thought that he might be losing the inner command, falling at last into Abomination."
Jessica defines the term for Ghanima (also in Children of Dune):
“Abomination,” the Lady Jessica had said, “our term for the pre-born, has a long history of bitter experiences behind it. The way of it seems to be that the inner lives divide. They split into the benign and the malignant. The benign remain tractable, useful. The malignant appear to unite in one powerful psyche, trying to take over the living flesh and its consciousness. The process is known to take considerable time, but its signs are well known.”
Ghanima considers: "This was a Bene Gesserit, and who knew better than they the history of Abomination?", which seems to contradict my original interpretation of "long were we warned ...". For Haleck possessed and abomination seem one and the same:
“You were to kill him only if he showed himself to be … possessed,” Halleck said. “Abomination.”
The preacher, when talking to Haleck about Leto:
He’s a community. As with any community under stress, any member of that community may assume command. This command isn’t always benign, and we get our stories of Abomination. But you’ve already wounded this community enough, Gurney Halleck. Can’t you see that the transformation already has taken place? This youth has achieved an inner cooperation which is enormously powerful, that cannot be subverted.
at which point the Paul within Leto clearly has the overhand, but is benign and helps Leto. The Preacher also call abomination "Bene Geserit nonsense".
Ghanima talking about Leto to Farad'n: "He gives more than anyone ever gave before. Our father walked into the desert trying to escape it. Alia became Abomination in fear of it." "Hypnotic suppression under stress linked to the wooing of a benign ancestor had saved Ghanima [from Alia's abomination fate]. They might have saved Alia. But without hope, nothing had been attempted until it was too late."
And then Leto II is an abomination if you interpret his word treachery as lying:
“Well and good, cousin. She asked me if I were Abomination. I answered in the negative. That was my first treachery. You see, Ghanima escaped this, but I did not. I was forced to balance the inner lives under the pressure of excessive melange. I had to seek the active cooperation of those aroused lives within me. Doing this, I avoided the most malignant and chose a dominant helper thrust upon me by the inner awareness which was my father. I am not, in truth, my father or this helper. Then again, I am not the Second Leto.”
In "God Emporer of Dune" Leto has the following exchange with Chenoeh:
“It was a design of our genetic history and the working of the spice. My twin sister, Ghanima, and I were awakened in the womb, aroused before birth into the presence of our ancestral memories.”
“Lord … my Sisterhood calls that Abomination.”
“And rightly so,” the Lord Leto said.
Which is not referring to being possessed at all.
Different uses for the same word by different people, by the same people. Maybe intentional by Frank Herbert, maybe a result of the complexity of such an epic tale. Sometimes I feel the need to analyse this, at others I just enjoy the complexity and things being not-so-clear-cut as I think that makes the original Dune books so much more thought provoking, than a simple, boring, storyline would.
¹ This is the second use of abomination in the book the first is by Yueh to describe the Harkonnen action against the Atreides
² This fact contradicts point 2 in Omegacron's answer
³ These are the thoughts of Leto, after he and Ghanima let their parents briefly "surface" in order to learn how to prevent what happened to Alia.