I think I found your problem. You've connected to output B whilst using the +/- inputs for A (assuming you are using the LM358 as the schematic suggests). With the inputs for B floating it is likely swinging its output at some high frequency making it look like the output is on. Connect your LED to the correct output and tie the inputs of B to the rails.
additionally:
from what I can see it looks like you have your Tx & Rx diodes the correct way around buts its worth double checking.
The other thing I noticed is that you have pins 2 and 3 swapped compared to the schematic, was that intentional and why have you done that?
The LM358 can only sink 8mA (while it can source 20mA) I'd question if that's sufficient current for your LED, but as you say its stuck in the on state so I guess it must be.