Languid implies sort of seductive or sensual. You could say that a beautiful woman moved languidly which implies slowly and seductively. Drowsy is more sleepy. Lazy is like someone who tries to avoid work. Indolent is moving as little as possible.

Languid has more of a swampy feel to it. Languid water, ect. It's used to imply being relaxed, or being slow due to sickness. It's a heavy, fluid word that is not often used except in prose.