When you first wrote, “Jimmy and me went to school,” the teacher said it should be “Jimmy and I went to school.” Okay. So far so good.
Then you wrote, “The teacher erudicated Jimmy and I.” Nope. It should be, “Jimmy and me.” The way to figure it out is to leave Jimmy out of it. Which pronoun would you use? “I went to school.” “The teacher erudicated me.”
If that happens, by the way, you should definitely report the teacher. Anyway the pronoun has two forms, the subjective case and the objective case, in Latin the nominative and the accusative, and people call them all kinds of other things.
In Latin and Greek and related languages, nouns all have different endings depending on their use in the sentence, whether it’s the subject or the object or a possessive, or the object of a preposition. In English the nouns don’t change but the pronouns do.
“The teacher gave salacious materials to Jimmy and I.” Again, you should report the teacher, but here the noun ‘Jimmy’ (which doesn’t change cases) and the pronoun ‘me’ are both objects of the preposition ‘to.’
“The teacher gave salacious materials to Jimmy and me.”
Okay, so now you write “He is taller than me.” It looks like ‘than’ is a preposition and ‘me’ is its object, which would be correct, but actually ‘than’ is a conjunction like ‘and,’ ‘but,’ ‘for,’ or ‘so,’ (or because, when, if, until, etc.) so it introduces a clause (with a subject and a verb) instead of taking an object (a noun) the way a preposition does.
Not only that, but the clause is an elliptical construction, meaning something is left out because it’s understood.
“He is taller than I (am).”
Same with as: “He is as rambunctious as I (am).”
I’ve done a lot of subbing, and once I told some students about elliptical constructions, and I heard they had some fun later with their regular teacher when she told them their sentences were incomplete. They just said, “Oh, no. That’s just an elliptical construction.”