Random values of voltage near ADC in current loop
The circuit has oscillations because parasitic inductance and capacitance is less on the PCB, and on the breadboard the RLC pole was at a point where the circuit didn't oscillate. 

It's hard to say exactly where to put the capacitance,these circuits are difficult to analyze by hand. I would first try capacitors on R11 and R12 as it's easier to create filters on the input. This would form a low pass filter so calculate the RC time constant and set it below the frequency of oscillation (and hopefully this is outside the bandwidth of your current signal).

As a side note: I didn't see anything for matching between the optocouplers in the datasheet, optocouplers can have a transfer function that varies widely even on the same part (the Ic/If ratio can vary from 63 to 125% on the ILD206) it may be advantageous for your application to use a part like the HCNR200 where the photodiodes and LED's are guaranteed to be matched if you need to back calculate what the current is through the current loop. (Or you could also calibrate each circuit)