Greek river becomes blocked, by the sound of it (4)

I believe the answer is:
styx
'greek river' is the definition.
'styx' can be an answer for 'river' (mythical river). I'm unsure of the 'greek' bit.
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for styx that I've seen before include "Underworld river ferried by Charon" , "River Charon rowed on" , "Hellish current" , "The last river one crosses" , "Hell's river" .)
