The LM358 is not a rail to rail opamp. With the negative power rail of the opamp connected to ground, the circuit has a hard time stabilizing when the input voltage is zero. Also, it IN- goes more positive than IN+, the circuit can never stabilize, as it cannot drive the output negative.
Try removing R11 connection to ground and connect it to a small positive voltage, like 1 to 3 volts from a battery. (By biasing the input with a dc offset, you give it some headroom and move away from the rail. ) If the oscillations go away, then you know its a headroom issue.