N4-N5: You only know modern, standard, semi-polite Japanese and possibly basic casual Japanese — without any contractions or slang or anything. The grammar covers the very basics of the most common grammatical words (と、は、が、を etc). The vocabulary's almost completely useless. After this level you can't understand any "real" Japanese and you certainly can't read the average manga or really make yourself understood in any way. I'd guess that you can understand 10-20% of the words from an average text.
• Textbooks: Genki 1 & 2 together; presumably any "beginner's" textbook.
• University: Years 1-2 in the USA, France, Germany; Year 1 in Sweden.
• In English terms: "I have an old dog. I am a boy. I was sad."
• You can easily understand: http://botsan.com/botsan.htm
Practice for this level:
— Ni no Kuni (二ノ国) for the NDS (not PlayStation); has furigana & is about 1/3rd voice-acted.
— Animal Crossing New Leaf for the 3DS; has furigana.
— Pokemon Gold/Silver/Crystal (GBC), Sun/Moon (3DS). The other games are more difficult.
— (Anime) Pokemon (1st season), Kobayashi's Dragon Maid
N3: You start learning synonyms for stuff you already know how to say (ex. multiple ways to say "but, however"), more usages of the same grammatical words, and more polite and impolite forms. So now for example you might have a chance at understanding the shopkeeper's very polite speech. I'd guess that you can understand around 30-50% of the words from the average text.
• University: Years 3-4 in the USA; Year 2 in Sweden.
• English: "I was sad because he died. The dead him sent me a letter."
— (Anime) Chobits
N2: This is THE MOST USEFUL LEVEL in vocabulary if you want to actually know real Japanese - most words in the average manga, anime, novel and newspaper come from N2-N1. You end up learning even archaic verbforms, and polish off most of the stuff that was confusing you before. It should be pretty easy to just pick up a manga and figure out the contractions, but you still have dialects, super-impolite/slangy things and stuff that you haven't learnt. You'd understand 70-80% of the average text; probably 95% if it's shoujo.
• Textbooks: A Dictionary of Intermediate/Advanced Japanese Grammar; 留学生のためのここが大切文章表現のルール
• University: Year 3 in Sweden. Assumably isn't reached in the USA unless you get a Master's.
• English: "It was unfortunate that he died very young, but when the dead him sent me a strange letter I was surprised."
• You can easily understand: Chobits: https://animelon.com/series/Chobits
Practice:— The original .hack// games (about 2/3rds voice-acted; parody mode after you've beaten the real mode is way easier to understand than the real mode)
— (Anime) Parasyte, Hunter x Hunter
N1: After the vocabulary from here you can read the average text meant for adults with relative ease; the vocabulary is mostly "detail-giving" words (ex. instead of "sickness" it's "diabetes") and consists of a lot of synonyms with nuanced meanings, and a lot of words where the meaning or pronunciation isn't at all obvious from the kanji. The grammar is a bunch of phrases, mostly where the meanings aren't at all obvious and most likely wouldn't be obvious even in example sentences. I'm not there yet but I assume you'd understand 90-100% of any given text.
• Textbooks: A Dictionary of Advanced Japanese Grammar
• University: Assumably isn't reached anywhere unless you get a Master's degree.
• You can easily understand: Parasyte: https://animelon.com/series/
— Sims 4; (Anime) Psycho Pass
After N1: Most likely you still have to learn puns/cultural references, slang, dialects (basic differences from them appear a LOT in anime/manga etc) and phrases, as well as perfect your polite/rare vocabulary.
• Textbooks: You've gotta find something in Japanese, ex. reading comprehension training books.
My Advice: Learn N1-N2 vocabulary FIRST, don't even worry about the other levels. You'll learn all the lower-level vocabulary automatically when reading manga and stuff, it shows up so often. Look up grammar as you need it but learn all the really informal stuff first and then gradually move on to more and more polite speech. Polite speech is literally just more words suffixed onto the impolite forms, or replaced words compared to the impolite forms, so it's incredibly stupid of textbooks to teach it before teaching impolite stuff.