The word comes from otaku spending more time at home on their hobby than hanging out with their friends, which encompasses things that would be called enthusiast or freak in English too.
That's not true. The word otaku, while it originally means "your home", is used as a polite second person pronoun; "you". When used by men in their 20s it can be considered as too polite, to the effect that it sounds something that a socially awkward people would use. There's some other forms of "otaku speak": using the honorfic "shi" (氏) instead of the commonplace "san". This, too, sounds too formal, and thus awkward.
The word "otaku" to refer nerds was coined by the writer Akio Nakamori in his essays, who used the word to refer to nerdy young males who used awkward language like that.
