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Could Voldemort have used an elf to side-along apparate Harry with him, and take Harry to Voldemort? Since any elf could apparate directly in and out of Harry's house, as seen in Chamber of Secrets.

Presumably it has something to do with Harry living with actual family. That loving bond the Dursleys evince every day for our young hero!

Sure, the Dursleys did not like Harry, and Aunt Petunia, I believe, despised him in a very special and visceral way that borders on pathological anti-thaumism, the irrational hatred of magical folk. Even so, Harry was safe while living in the Dursley's home. He kept going back every summer holiday. They did provide for him (basic physiological needs, apparently apart from love). They may have hated him, but their presence was a protective magic probably deeper than any mere wand or elf magic could contend with.

We could go one more and ask why not just let Harry grow up in Dumbledore's office? He'd be safe and among wizard folk. But we'd be back to the family connexion issue.

That is something Voldemort could do, but probably something he would not do. As Dumbledore mentioned in HBP, there are somethings (power of love for instance), that Voldemort considers to be below him to be worth giving any attention. From DH we also see that Voldemort made a very critical mistake in not realizing Kreacher could have the ability to aparate out of his cave after drinking the potion. Also from HBP, we know that Voldemort likes grandeur in everything he does, which is the reason he wants the Hogwarts founders' personal items for his horcruxes, and not mundane everyday objects. It's also the reason he hatched the elaborate year long plan in GoF to smuggle Harry pout of Hogwarts instead of trying a simpler more practical approach. So keeping these things in mind,

1. It's possible it never crossed his mind to use a house-elf to aparate Harry out of the Dursley's house (I's guessing this is where you mean by 'Harry's house'), or it's also [ possible Voldemort didn't know this could even be done, as he has been shown to be unaware of the details of house-elf magic




2. The method is simply too boring for Voldemort's tastes. He would rather take out The Boy Who Lived in a manner that would further emphasize his power over the kid

However, I think the more likely explanation is that it was simply due to the protection offered to Harry at the Dursley's against Voldemort. The Dursley's house was not protected against aparating, Voldemort could have as well sent any human DE to the house to side along aparate Harry with him. It seems Harry was protected at the Dursley's house not just directly against Voldemort, but also against any of his goons that might attack him there on Voldemort's orders, as we don't see Voldemort ordering any of the DE to attack Harry there either. I think that as far as Harry's protection at Privet Drive is concerned, Voldemort ordering a house elf is not any different from him ordering a DE to kidnap Harry, and so the protection magic would have saved Harry from anything Voldemort could have done.