How does this circuit read 4-20mA current loop input through Op-amps?
120E is just \$120\Omega\$. If you look at J11, it's putting a \$120\Omega\$ resistor in the current loop. So this means, at \$4mA\$ the drop will be about \$480mV\$ and at \$20mA\$ the drop will be about \$2.4V\$. This voltage is applied to the (+) input of U4A via a negligibly small \$10\Omega\$ resistor, so the opamp then attempts to change its output so that the (-) input equals that input voltage. (It follows the input.)

You get to decide how you want to handle these things. If there is no current, then the output will be close to \$0V\$ and you may care about that. If there is something near to \$4mA\$ drive, then you will see about \$500mV\$ present. If \$20mA\$ then near to \$2.4V\$. All within range of your converter, I suspect. That's what P1.0 should see.



LATE EDIT:

The relevant circuit for your \$4-20\:\textrm{mA}\$ subcircuit is the following (and not as you diagrammed it):







simulate this circuit &ndash; Schematic created using CircuitLab

I've kept the capacitors in place so that all the details are present and can be used to double-check my work. But you can ignore them for the purposes of figuring out where to put the meter.

One lead of the meter should be attached to ground. This means anywhere that's convenient. Note that J11.1 is attached to ground. So you could use that pin or anything directly connected to it for this purpose. You could use the ground end of \$R_{15}\$, if that was easier for you. You could use the (-) supply pin of the LM358 if that was easier. If you have a question about some "convenient" bit of metal available to you, then just measure the Ohms from that spot to J11.1. If it is very close to \$0\:\Omega\$, then chances are you are okay using that convenient spot.

The other lead of the meter should be attached to the place of interest. In this case, I think you want any pin or end of a device that is attached to P1.0. This could be the non-ground end of \$C_{18}\$ or the non-ground end of \$R_{21}\$ or the output pin of the LM358 (pin 1) or even its (-) input pin (pin 2.) If you have any question about which end is which, just check again by measuring from the point you aren't sure about to J11.1. If it is very close to \$0\:\Omega\$, then it is NOT the correct end and you need to consider the other end of it as the one you probably want.