I understand that House-Elves really do want to serve but is it really what they want or would they prefer to be freed? This whole concept is really odd to me and I don't know how it is supposed to be. Do they love their family? Do they pay attention to abuse? How does it work? I can't figure it out.
Most of them find satisfaction in serving their masters BUT that's part of the horror of enslavement.
From the point of view of a free person, the fact that a majority of house-elves seem happy with their fate is puzzling, but it is actually a part of the vicious mechanism that perpetuates the system.
1/ The idea of freedom itself
House-Elves are born and raised as servants. All the other House-Elves they know are servants. This is the only model of existence they have. Their social scope is mainly limited to their own family and the wizard family they are serving, and Wizards make sure they only leave home for specific tasks. In these conditions, what would even mean "freedom" for an House-Elf? The modern ideas of freedom, democracy, equality, have been progressively shaped in the past centuries, and required education of the people to be widespread. It's not something that pops out of nothing easily.
2/ House-Elves' culture.
After centuries of - often violently - enforced bondage, House-Elves have developed a culture based on self-devaluation, worship of wizards, pride of well-accomplished work. In their restricted social circles, the worst shame they can think of is to be freed by their masters. In addition to be worthless, they'd end up being useless. Anyway, they would have no place to go, find no work (what family would accept a freed elf?), and probably die or worse (at least this is what they imagine). They may not be aware that Hogwarts is a last-chance refuge for homeless Elves, or at least it was when Dumbledore was Headmaster. Being a good servant, on the other hand, is a promise of peer recognition and safe future.
Many House-Elves are constantly threatened of violent punishment and social exclusion. As any sensible being in similar situation they develop coping strategies to survive, including self-denial, chronic anxiety, submission (as in the "Uncle Tom syndrome"), traumatic bonding… This, naturally, contributes building the "House-Elf culture", to the point Wizards do not even need to be violent anymore. "Kind" families benefit from a well-internalized domination system, where the oppressed are grateful to their masters for not being too violent.
You can add if you want the magical bond that guarantees their obedience and loyalty. However I'm not sure it is absolutely necessary. Sociology and psychology might be enough…
All House Elves enjoy serving a family that is kind to them
“Sirius was horrible to Kreacher, Harry, and it’s no good looking like that, you know it’s true. Kreacher had been alone for such a long time when Sirius came to live here, and he was probably starving for a bit of affection. I’m sure ‘Miss Cissy’ and ‘Miss Bella’ were perfectly lovely to Kreacher when he turned up, so he did them a favor and told them everything they wanted to know"
-Hermione Granger, Harry Potter and the Deathly Hallows
Kreacher betrays Sirius even though he is his rightful master. Bellatrix and Narcissa probably manipulated Kreacher through kindness. Kreacher betrays an unkind member of the Black family for an kind member(kind to him and appreciative) of the same family.
Dobby was treated poorly by the Malfoys.
“Dobby hid and watched for Harry Potter and sealed the gateway and Dobby had to iron his hands afterward” — he showed Harry ten long, bandaged fingers — “but Dobby didn’t care, sir
So he betrayed his master to help Harry, who was good to him. Dobby responds even when he isn't called; when Harry calls Kreacher once, both Dobby and Kreacher appeared. If Harry had wanted Dobby for himself, Dobby would have probably accepted his ownership.
Winky is devastated when she is fired from Crouch's service.
Therefore, house elves wish to serve those who don't mistreat them. And they wish to serve rather than remain free, provided they aren't mistreated.
Your question indicates your realization of the obvious parallel between house-elves and human house slaves, of a race other than the masters'. Naturally, you're baffled by why a slave would enjoy serving his master, even with the option of being freed; or, more importantly, why Rowling, herself and through her protagonists, describes this is reasonable and commendable.
In my opinion, Rowling wanted to eat her cake and have it with the house elf-slaves: She wanted Potter & al to free them, but at the same time it seems she couldn't resist keeping them, or at least dobbie, as his servile self. So, the freed slave stays on as a happy pseudo-free servant.
It's not that this phenomenon is unknown in human history. I recommend you listen to an important speech by black liberation struggle activist, Malcolm X, called The House Negro and the field Negro (emphasis mine):
To understand this, you have to go back to what the young brother here referred to as the house Negro and the field Negro back during slavery. There were two kinds of slaves, the house Negro and the field Negro. The house Negroes--they lived in the house with master, they dressed pretty good, they ate good because they ate his food--what he left. They lived in the attic or the basement, but still they lived near their master; and they loved their master more than their master loved himself. They would give their life to save their master's house--quicker than the master would. If the master said, "We got a good house here," the house Negro would say, "Yeah, we got a good house here." Whenever the master said "we," he said "we." That's how you can tell a house Negro.
If the master's house caught on fire, the house Negro would fight harder to put the blaze out than the master would. If the master go sick, the house Negro would say, "What's the matter, boss, we sick?" We sick! He identified himself with his master, more than his master identified with himself. And if you came to the house Negro and said, "Let's run away, let's escape, let's separate." The house Negro would look at you and say, "Man, you crazy. What you mean, separate? Where is there a better house than this? Where can I wear better clothes than this? Where can I eat better food than this?" That was that house Negro. In those days he was called a "house nigger." And that's what we call them today, because we've still got some house niggers running around here.
This modern house Negro loves his master. He wants to live near him. He'll pay three times as much as the house is worth just to live near his master, and then brag about "I'm the only Negro out here." "I'm the only one on my job." "I'm the only one in this school." You're nothing but a house Negro. And if someone comes to you right now and says, "Let's separate," you say the same thing that the house Negro said on the plantation. "What you mean, separate? From America, this good white man? Where you going to get a better job than you get here?" I mean, this is what you say. "I ain't left nothing in Africa," that's what you say. Why, you left your mind in Africa.
Rowling legitimizes the house negro, uses him to glorify her supposedly benevolent and moral protagonists - and that's one of the reasons I deeply dislike the Harry Potter series.
Elves genuinely enjoy being servants.
The most extreme example of an elf who enjoyed freedom and independence was Dobby, and even he had his limits, preferring the rigeour of work to all-out liberation.
"And Professor Dumbledore says he will pay Dobby, sir, if Dobby wants paying! And so Dobby is a free elf, sir, and Dobby gets a Galleon a week and one day off a month!"
"That's not very much!" Hermione shouted indignantly from the floor, over Winky's continued screaming and fist-beating.
"Professor Dumbledore offered Dobby ten Galleons a week, and weekends off," said Dobby, suddenly giving a little shiver, as though the prospect of so much leisure and riches was frightening, "but Dobby beat him down, miss...Dobby likes freedom, miss, but he isn't wanting too much, miss, he likes work better."
(Goblet of Fire, Chapter 21, The House-elf Liberation Front).
Hermione expressed hopes that Dobby's example would lead to a change of mentality from other elves, at least those at Hogwarts.
"I think this is the best thing that could have happened to those elves, you know," said Hermione, leading the way back up the marble staircase. "Dobby coming to work here, I mean. The other elves will see how happy he is, being free, and slowly it'll dawn on them that they want that, too!"
(Goblet of Fire, Chapter 21, The House-elf Liberation Front).
However, he was viewed by wizards like Hagrid as a strange exception to the traditional love of house-elves to serfdom.
...[Hagrid] flatly refused to join S.P.E.W. when [Hermione] showed him her badges.
"It’d be doin' 'em an unkindness, Hermione," he said gravely, threading a massive bone needle with thick yellow yarn.
"It’s in their nature ter look after humans, that’s what they like, see? Yeh’d be makin' 'em unhappy ter take away their work, an' insultin' 'em if yeh tried ter pay 'em."
"But Harry set Dobby free, and he was over the moon about it!" said Hermione. "And we heard he’s asking for wages now!"
"Yeah, well, yeh get weirdos in every breed. I’m not sayin' there isn’t the odd elf who’d take freedom, but yeh’ll never persuade most of 'em ter do it – no, nothin' doin', Hermione."
(Goblet of Fire, Chapter 16, The Goblet of Fire).
As for the elves themselves, they take a lot of pride in their work. They regard unemployment as the height of dishonour and see servitude as their life's goal. They have no other ambitions or dreams. This is made perfectly clear in their exchange with Hermione.
"Begging your pardon, miss," said the house-elf, bowing again, "but house-elves has no business to be unhappy when there is work to be done and masters to be served."
"Oh, for heaven's sake!" said Hermione angrily. "Listen to me, all of you! You've got just as much right as wizards to be unhappy! You've got the right to wages and holidays and proper clothes, you don't have to do everything you're told - look at Dobby!"
"Miss will please keep Dobby out of this," Dobby mumbled, looking scared. The cheery smiles had vanished from the faces of the house-elves around the kitchen. They were suddenly looking at Hermione as though she was mad and dangerous.
"We has your extra food!" squeaked an elf at Harry's elbow, and he shoved a large ham, a dozen cakes and some fruit into Harry's arms. "Goodbye!"
The house-elves crowded around Harry, Ron and Hermione, and began shunting them out of the kitchen, many little hands pushing in the smalls of their backs.
(Goblet of Fire, Chapter 28, The Madness of Mr Crouch).
The suggestion of wages, holidays and freedom from work is greeted with outright hostility. The elves don't want freedom. As Hagrid said, it's in their nature.
House elves were born into servitude to witches and wizards, so I suspect that freedom is something that isn't tangible, it is mysterious, and like humans, house elves are afraid of the unknown. Since they were born into serving and have been doing such for hundreds of years, they must have adapted into taking pleasure in constantly serving their masters. Also, to prove my point about fearing freedom we have Winky as a perfect example: as soon as she is free from Mr. Bagman she turns to drinking butterbeer which might not be as potent as alcohol for humans, however, it is quite potent enough for house elves to wash away their feelings. But something to contradict what I said about fearing the unknown is Dobby; who takes great pleasure in being free, but I believe he is one of a kind because when Harry, Ron and Hermione enter the kitchens all the other house elves working for Hogwarts were avoiding Dobby and Winky. Finally, when Hermione sets out knit hats in the Gryffindor common room all the house elves (excluding Dobby) feel scandalized and refuse to clean Gryffindors common room. In conclusion I do believe that house elves genuinely enjoy serving their masters. To make a note about Kreacher, he was always loyal to the family Black but, I think he strongly disliked Sirius because he was blasted off the family tree and consequentially, even though he does not feel like Sirius is family, he is still magically bound to him.