I see it most often used to mean torpid, inactive, listless, etc. But it certainly also means effortless, elegant, relaxed, etc. That said, I think of the former meanings when I see the word until I hear the context. Languish is the verb form which means loss of vigor, or to suffer neglect or inactivity, etc. Languish doesn't have any positive connotations that I'm aware of.

It can be positive or negative, depending on the context. I see this word used most in a sporting context, particularly football. Apologies if you're not a football fan but I'll give an example to try and illustrate how the word can be used. There was a player for Manchester United a few years ago called Dimitar Berbatov. Now, I saw this word used to describe him more than probably any other player. He was a very technically accomplished player, very skillful and he seemed to do very difficult things without any effort. 'Languid' was often used in a complimentary sense to describe the way he played the game. However, in some quarters, perhaps when the team wasn't playing well, his style of play was used against him as a criticism. He was sometimes criticised for not running about as much as other players, as though this 'languid' style of play meant he wasn't trying as hard as the others. This seems to tie in very well with the descriptions offered by the dictionary, it can be used in both a positive and negative sense, to show someone can do things elegantly and without effort, or alternatively to hint they are lazy and aren't trying very hard. Edit: I don't know if you're a tennis fan, but someone like Roger Federer could be described as having a languid style of play. As opposed to someone like Rafa Nadal who appears to exert himself much more on the court.

Well, I wouldn't say "languid" has a positive nor negative connotation. It's more like a smooth, flowing movement, like water gently flowing down a small creek. It really depends on whether you want someone to hurry up (Annoyingly languid because they're being slow and you'd like them to go faster) or if it's like, sexy or elegant, although I'd say it's more commonly used to describe something sexy or slow-paced.