This is not a complete answer, only a loose collection of some first, unordered thoughts.
Many of the authors of current best-selling fiction are script writers. Examples are George R. R. Martin (before he wrote A Song of Ice and Fire he worked as a script writer for Twilight Zone), Anthony Horowitz, Michael Crichton (Universal bought the movie rights to Jurassic Park before the book was published), and many others.
You can take this to mean that they are so good and talented they can word in both worlds. You can also take this to mean that they write their novels to be turned into film or tv shows, and that they have the connections to make this happen.
I'm not sure any of the three books you mention were immediate mega sellers. I believe they slowly accumulated notoriety and have become the huge successes they are only because they have "added up".
For example, Wikipedia says the first volume of the Hunger Games appeared in 2008 but became a number two (sic) bestseller only in the summer of 2012 – that was when the trailers for the movie adaptation began running, so the movie and the novel were sort of marketing each other. Later, the second and third part of both movie and novel where advertising for the first, second, and third part of movie and novel – six products on the market that made each other popular: when there is some hype around volume two of a movie series, many people go check out volume one of the book. Another factor that keeps adding sales to the Hunger Games is all the latter rip-offs that are marketed as being like the Hunger Games. Go to the YA section of a bookstore or library and read the front and back cover. Half of them will say that fans of the Hunger Games will enjoy that book, or that the book is "Hunger Games + something". So if you are new in that section of the bookstore or new to YA, you'll hear Hunger Games here, Hunger Games there, and eventually you will buy and read it. Finally, after a certain level of fame, people will read it just because everybody is talking about it. Look at the reviews on Amazon. Sure, its only about 3% one-star reviews, but 3% of 55,000 reviews means that 1650 disliked that book, and many of those reviews begin with something like "everyone said this is a good book, so I picked it up and was disappointed". And that is only those that wrote a review. The Hunger Games sold more than 20 million copies (all three volumes combined, I think), so maybe 600,000 people picked it up because "someone said it was good" and then where disappointed. That is more disappointed booksales that most books sell ever. So just the hype added hundreds of thousands of sales to people who don't like that kind of book.
The more books you sell the more books you sell.
I think for a book to become a bestseller, that is, to start selling outside the core genre readership who read everything in their niche, it has to have something that speaks to the people of that time.
The Hunger Games were published at a time when reality tv shows has begun to send people into survival camps and prince-of-persia-like action-riddle camps. Before 2000-something, reality tv was about people doing stuff in their normal lives, or people trying to become media stars, but a few years before the Hunger Games there was a wave of young, halfnaked people being sent to tropical islands or former prison islands or the jungle and having to fight to stay alive or fight an opposing group. So that was in the air, the "hunger games" of the Hunger Games.
Also there had been a decade of high school shootings, that is teenagers engaged in mass murders of teenagers. There had been a decade of heated discussion about violent video games. Virtual reality (World of Warcraft, Second Life) had happened in those ten years. That was the media debate the target audience had spent their puberty in. They grew from kids to adults in a world where everyone was concerned about adolescents and violence in the media turning into violence in real life.
A book about teens sent to a game to kill each other was just hitting the right nerve.
Not least, because to many teens experience adolescence as a kind of battle zone.
Reading how-to-write books, the Hunger Games does everything right. I have been accused of always and only using the Hunger Games as an example whenever I answer questions, but (the first volume) is so perfectly done that I find it hard to find a better example.
The stakes are high (death; later: save everyone). But the abstract (save everyone) and selfish (save herself) stakes have been made concrete and selfless through a stakes character: save Primrose, then save Peeta, then her family, and the family of Rue, and in that way the stakes slowly expande to saving the world, instead of starting with that rather preposterous goal, so that it appear natural and unassuming. The protagonist has greath strength and a fundamental flaw she has to overcome (she cannot love or trust, except her sister). Overcoming that flaw (and loving Peeta) is the solution to her quest. That her love is faked is a nice twist, although we all know it isn't (a double twist). That she loves both Peeta and Gale (or rather, both loves and doesn't love both) is the perfect triangle, and by the third volume both Peeta and Gale have turned into the wrong boy, another nice twist. Katniss has been hurt: death of father, alcoholic mother, poverty, opression – there is something for everyone to identify with, but it never lays on too heavy, because Katniss doesn't let it get her down (her strength). Katniss also goes the proverbial hero's journey. She even litterally goes through the underworld (the game) and has to die (the berries). There is the refusal of the call (Katniss goes hunting on the morning of the reaping), the mentor (Haymitch), the supernatural aid (the flying presents), and so on.
But most of all the Hunger Games is written like a movie script: mostly show-don't-tell, little interiority, focussed on character interaction and action. It must have been easy to sell that book to Hollywood.
I do think that the Hunger Games is original. Nothing in the book is new, but when you compare it to the YA dystopia that came before it (The Giver, Mortal Engines, Uglies) they are all very tame and slow so that the violence of the Hunger Games (the book, much of it is missing from the movie) hits you like a hammer. The Hunger Games is the first YA for adults, or adult fiction for teens. It brings together something from both categories and creates something new. To me (and I may be mistaken, because I haven't read every book out there) the Hunger Games was the first book in a new subgenre that the Maze Runner, Divergent, and others then have followed into. I would call that genre "YA dystopian action adventure romance", or some such.
Twilight isn't badly written either. It employs simple language and simple thoughts, which makes is accessible to all those millions whose IQ isn't 125+. You have to remember that the majority of people are, to be blunt, too stupid to understand what is going on in the world or in their own lives. Ride a bus and listen to people talk and you will realize that if you want to sell a large number of books you must write in simple English. Why do tabloid papers and idiot tv shows sell like crazy? Because they are stupid enough for stupid people to get them.
A bestseller must not be too intelligent or eloquent.
At the same time, Twilight isn't actually stupid either. It is simple, but not idiotic. Twilight is like the not so bright, but very warmhearted and friendly girl that is its protagonist. The whole book, despite dealing with vampires, leaves you with a warm glow. Edward's vampire family are very nice to Bella. I mean, think about it. Can you imagine Dracula's family being nice to Jonathan Harker? Twilight isn't about vampires, but about the shy outsider girl and the bad boy. It is an old story, but not in the vampire tradition at all. And when you come from reading teen romance, making the school's bad boy a vampire is acutally pretty original. I'm not such a teen romance reader that I would know if it has been done before, but if you look at the book from the eyes of the target audience (teen girls) instead of the history of horror literature, then you get an idea of how it might have been a fresh take on an old (love) story.
A bestseller must be original for its intended audience.
Do not underestimate marketing. While there are viral bestsellers that grow from word of mouth, it is simply not true that no one knows what makes a bestseller. A bestseller is made through marketing.
Paolini's Eragon became the huge success it is by being recommended by Oprah Winfrey on her show. His young age played a major part in how the book was received, the "wunderkind" always sells well.
I haven't read Harry Potter and can say nothing on it.