Why is the output signal of my amplifier heavily distorted?
LM386 needs an AC coupling capacitor on its input.

If your input circuit is DC coupled, you disrupt the input biasing arrangements built into the amplifier. Instead of being centred, the output voltage is probably close to one of the supply rails, clipping the positive or negative half of the AC waveform, resulting in severe distortion.

Insert 1 uF (or 10 uF) in the path labelled "Mono_Audio" on the schematic.

EDIT : Peter Mortensen is absolutely right to ask for references - my memory was way off here. 

What I got wrong : it is NOT essential to eliminate a DC path between +In (Pin 2) and GND.

What still matters : it IS important to keep the DC source impedances similar on both input pins (pin 2 and pin 3). to keep the inputs roughly balanced and the DC output voltage roughly Vcc/2 (4.5V wit a gV supply.

Since Vin- (pin 2) is connected to GND here, that means Vin+ must be fed from a fairly low impedance to GND, say 10K or less. So my previous suggestion may be a step in the wrong direction (unless you also allow Pin 2 to float) - instead, you may need a DC path to GND such as a 5K resistor from "Mono_Audio" to GND.

Be guided by the DC voltage on VOut (pin 5).