No one was ever upset by a little laughter after (him, he) or (her, she) had taken this treatment. Which ones are correct him, he, her, she in sentence?
This is a good question. Let me give you the correct sentence and then give you the reasoning behind the answer.
"No one was ever upset by a littler laughter after he or she had taken this treatment."
This sentence is a bit challenging, because the word "after" can be both a preposition or a temporal adverb that begins a temporal clause. In this case, it is a temporal clause. When we realize this, it becomes apparent that "he" and "she" are the correct pronouns to use, because what you need is a subject. The verb of the clause is "had taken."
The general rule of thumb is as follows. "He" and "she" are used when you need a subject or when you have a predicate nominative. All other cases require the object form, "him" or "her."