In The Movie, at least. The novel states that this is absolutely not the case, and that Eli does care for Oskar.
Why is Håkan jealous of Oskar? In the book it's clear he's a pedophile whom Eli keeps on a tight leash, but the movie audience can infer that Håkan met Eli the same way Oskar did.
Eli treats Oskar a great deal better than Håkan. There aren't any friendly interactions between Eli and Håkan in the movie - either yelling or jealousy. Even if Håkan and Eli once had feelings for each other and it had faded over the years, surely they would be closer. The book's explanation seems more plausible than that Håkan and Oskar are similar.
Crowning Moment of Heartwarming: When Eli shows Oskar what he looks like through her eyes: handsome and strong. Admit it, after all the crap he went through, and with all his insecurity, that was a welcome Mood Whiplash to such a dark novel.
Designated Hero: Oskar. While you can justify Eli killing people because she needs human blood for sustenance, he is just okay with her killing people, including his bullies, just because he doesn't have friends.
Esoteric Happy Ending: There are two outcomes of the ending; one is that Oskar takes on the role of The Renfield for Eli and procures blood for her for the rest of his life, the other (endorsed by Word of God) is that she turns him into a vampire. It's the closest thing to it for Oskar and Eli.
Fridge Brilliance: In the remake, Abby tells Owen to strike back hard against the bullies to get them to stop, and to use his knife if they keep harassing him. She then tells him that she will help him if all else fails. Owen's confrontation with the bullies plays out in that exact order: Owen strikes Kenny with a pole to defend himself. When the bullies return much later for revenge, Owen attempts to defend himself with his knife, but that fails, so Abby helps him. And boy, does she help him.
The puzzles. At first, it may seem like an ordinary child's hobby; however, vampire lore holds that vampires (and other supernatural creatures) cannot resist puzzles or riddles.
Fridge Horror: A rare instance where there is possibly more of this than straight-up scares.
In particular, the interpretation that Oskar is going to become Eli's new guardian... which directly implies that, since Eli is Really 700 Years Old, that Håkan could easily have been in the same position as Oskar was at one point. On the DVD commentary, John Ajvide Lindqvist says that he likes that the movie is ambiguous on this matter, but that it was not the story he intended when he wrote the book.
Also, Eli assures Oskar that she didn't steal money from people she's killed. She claims people gave it to her. How a pretty but androgynous 12-year old waif gets money from strangers is not explained. In the book, Håkan is a pedophile and that explains his attraction and devotion to Eli. So, the theme is still subversion to darkness or vices, but in a different way. Håkan represents the darkness associated with the fact of who Eli has to be to survive, while Oskar represents the light. Eli is more than fine with stringing Håkan along to get what she needs, and Håkan is a much more morally repugnant figure with less to pity than portrayed in the movie.
An easily overlooked detail in the original movie half explains this. One of the toys in Eli's apartment is a silver and gold Faberge puzzle egg. So presumably she has been hording wealth for centuries. Now where she got it in the first place....
This post discusses a rather dark interpretation of the significance of the Now & Later jingle in the remake.
Fridge Logic: How did that teenage pimp know Håkan was a pedophile just by looking at him?
It's mentioned that the place they were in was a relatively well-known spot to pick up child prostitutes. Håkan was looking around in a way that probably made the pimp guess he was there for that reason.
It's the Same, Now It Sucks: The remake has several scenes that are word-for-word from the original. This has not gone unnoticed. Especially since Reeves promised a new, different take on the novel and instead delivered another remake, complete with scenes and concepts that only existed in the Swedish film and weren't in the novel to begin with.
Moral Event Horizon: Jimmy and Kenny trying to kill Oskar (Owen) by drowning him in the school pool while the rest were distracted by a dumper fire. Even one of the other bullies felt was taking it too far.
Cranked up to eleven when Eli as he escapes nigh rape, unwittingly traps Tommy inside the completely dark bomb shelter together with Disfigured!Mindless!Zombie!Rapist!Vampire!Håkan for several hours. Tommy manages to pullthrough, but is clearly not all that well adjusted aftewards.
In the remake, Abby's vampire attacks are considerably more brutal and violent, leaving the victims a bloody mess, and yet still alive as she feeds.
The Woobie: Seriously, is anyone in this story not a woobie? Even the mean ones end up horrifically.
Trans Equals Gay: Considering Eli and Oskar's relationship a Queer Romance is contingent on accepting this trope's claim as well. Granted, claiming that Eli is "trans" is also highly dubious at best, since he didn't exactly choose to be castrated and there may be other reasons why he lives as a female. The book also clarifies that he identifies as male.