For example, the parts of a sentence that a preposition operates on are called "prepositional objects". I was wondering if there's a name for the parts that are connected by a conjunction? E.g. in "apples and oranges", would we say "apple" and "orange" are the objects of "and"?
They are its coordinands; see http://www.glottopedia.org/index.php/Coordinand.
(That page also lists some alternatives, namely term, member, coordinated unit, coordinate, and conjunct.)
elements: when a coordinating conjunction is used to connect all the elements in a series, a comma is not used:
Presbyterians and Methodists and Baptists are the prevalent Protestant congregations in Oklahoma.
equivalent sentence elements: Correlative conjunctions always appear in pairs -- you use them to link equivalent sentence elements.
elements: A coordinating conjunction joining three or more words, phrases, or subordinate clauses creates a series and requires commas between the elements.