I'm fairly certain L isn't on the spectrum. He's fine with eye contact and listens and converses well with Light. His interests and talents are spread throughout all academics and tennis. He understands motivations of Kira well, lies without a problem, and charms Misa fairly easily. (At first.) I don't remember stimming, just the thumb thing, and that isn't a repetitive movement. His speech is normal, and given that he's in a manga, we can't tell about voice fluctuation. He's not necessarily antisocial either, just in need of secrecy due to the nature of his job. So it could be explained that he's using his talents instead of committing the secrecy because he needs privacy. In fact, he was fine being handcuffed to Light, so I'd say either he's very good at hiding irritation, which he has no need for, or he's not too high on privacy.
Keep in mind that L is a genius detective. He has no need to impress society, especially given his isolation.