I think that there is no more differences between 聞く and 聴く than hear and listen. For my image, I think that 聞く is close to hear, while 聴く is close to listen. However, I guess we often use 音楽を聞くinstead of 聴く. We never use "訊く" in casual or formal writings. I guess that "訊く" might have strong meaning like demanding an answer.

when you hear something you can express "聞く" 子どもの泣き声が聞こえた。 こどものなきごえがきこえた。 when you listen something you can express "聴く" 音楽を聴く。 おんがくをきく。 先生の話をよく聴く。 せんせいのはなしをよくきく。 when you ask something you can express "訊く" わからないところを先生に訊く わからないところをせんせいにきく。 迷子になったので道を訊く。 まいごになったのでみちをきく。 but "訊く" is not common-use Chinese characters so we usually express "聞く"