What does 呢 do in 他在睡觉呢?
他在睡觉 is to state the fact he is sleeping, which may not necessarily imply anything.  

他在睡觉呢 adds a tone in the sentence, which often invokes some implications such as he is sleeping so he can't answer you now, he is supposed to do something else while he's still sleeping, and etc.  The implications are various based on the real context.  

Sometimes, 呢 is just to add a bit emphasis without any implications.他在睡觉呢 might just mean he is sleeping(underlying meaning: we should not bother him).  

Overall, context is essential for analyzing the underlying meaning or implications of the speakers.