Are there any subtle differences in meaning between anhören, lauschen, hinhören and hinhorchen, all of which has got something to do with listening?
Anhören focuses on the intent of listening.
Ich höre das Lied. (I hear the song.)
Ich höre (mir) das Lied an. (I intentionally listen to the song.)
Lauschen means to eavesdrop!
Sie lauscht. (She eavesdrops.)
Ich lausche dem Lied. (I try to figure out the gentle parts of the song.)
Ich lausche deiner Stimme. (I listen to your (gentle) voice. — either sweet-talk or sarcastic.)
She belauscht die Nachbarn. (She eavesdrops on the neighbors.)
Hinhören is intentional, careful and visible listening to something. It's similar to zuhören but points to an item which is not the speaker.
Ich habe eine Idee. Hör zu! (I have an idea. Listen to me!)
Die Tür quietscht. Hör hin! (The door creaks. Listen to it!)
Horchen means putting your ear very near to something which makes a sound.
Some dialects prefer it instead of hören and also use hinhorchen. It means the same as hinhören then. Similar for abhören.
Horch mal! (Listen to me carefully!)
In other dialects horchen is a synonym for lauschen instead.
Horch mal! (Put your ear here and listen carefully!)
DID YOU KNOW? The car brand Audi is named after its founder Horch, after he was dismissed from the first car company he founded under his own name. Audi means Listen! in Latin, so does Horch! in German.
Lauscher and Horcher are common comical names for the ears.
Sperr mal die Lauscher auf. (Listen! – literally: Unlock your eavesdrop-tools.)