It's not uncommon for a student to be really good at grammar but completely unfamiliar with the language of 19th Century. The challenge is to learn how to make educated guesses about the meaning of unfamiliar words from context. If you are not someone who used to read as a child, the vocabulary used in 19th century texts often contains words that we use today, but we use them differently. So, it's easy to be to be misled.
For example: the word "directly" used to mean "right away, now, without wasting time" as in when speaking to someone waiting in line. "I will be with you directly." Current usage of the word "directly" is different. It means "without intermediary, or middleman." As in, "I get my eggs directly from the farm stand; I don't buy the from a grocer.
In addition to the benefit of having read widely as a child, those students who have studied a foreign language have an advantage. If you don't speak the language, you have nothing but context to understand what's going on. Thus, you have had lots of practice with this skill. When you study foreign languages, you get really good at guessing the meaning of words from context. Are you buying a cup of coffee or are you being told you can't ride the tram without getting a ticket from the machine on the corner? Context provides clues to what is being said.
Think about how the language of previous centuries is different: it is like a foreign language, so use the same learning strategies. It would be great if you could read more, but most students have too much homework. They don't have time to add more reading.
If you haven't read much, you will lack the cultural references and social mores being referenced in the questions on the SAT. You must know how to "read between the lines" for what is implied. To understand unknown words, and phrases, look at the surrounding context: the sentences before and after, the storyline, the subject of the passage.
However, to become really proficient at understanding idioms, phrases and words that are foreign to you, need to hear the intonation. It provides emphasis that often makes the meaning clear. But you can't get the intonation from a book. So here's a tip.
TIP: The best way to learn how to understand 19th Century texts is to listen to audio books: books which have been read aloud by professional readers who are providing the right intonation, because not only do you have the story to guess from, you also have the the intonation, the inflection and the emphasis of the reader.
By contrast, if you're reading the book, it's pretty much flat. You have context, but it's much more challenging. You simply don't have as many clues as when you have an audio version of a book. This is not a little skill you learn in a day. It's a habit that will enrich your studies and make your life more interesting and enjoyable.