Now we know the baud rate - you did mean 2400? - C4 is far too big. 4.7 nF is enough. (According to my LTSpice simulation, anyway.)
This is with a 0.3 V amplitude signal from the pick-up coil (simulated with a signal generator and modulated by a switch).
It shouldn’t be oscillating, it should be resonant, if that’s the frequency that the meter sends out. If it’s oscillating on its own, you won’t be able to detect the signals from the meter.
If it is oscillating on its own, you might need a large electrolytic in parallel with C5 - 22 μF, or a damping resistor in parallel with the coil.
BTW, it’s normal, when drawing a circuit diagram of this sort of thing, for the signal to go left to right.