OP Amp - Finding currents
I know that V- ≠ 0


Bad assumption because negative feedback is being used and negative feedback attempts to maintain the two input voltages at the the same potential. Given that the non-inverting input is 0V then it is safe (for a theoretical assessment) to assume the voltage at the inverting input terminal is also 0V.

You then have to ask your self what voltage does the output have to produce to give 0V (equilibrium) at the inverting input. Clearly the voltage at the junction of the 10, 20 and 40 ohm resistors has to be -4V (by visual inspection and simple brain math) but you can work that out by ignoring the 10 and 40 ohm resistors and imagining what voltage needs to be on the 20 ohm resistor terminal that makes 0V at the inverting input.

I'll leave the rest for you to solve because you've had more than enough hints.