Why does this circuit produce a static noise?
Some comments:
I constructed initially with only one transistor (BC107) and tested by giving audio signal as input. The output from the 8 ohm speaker was pretty much distorted, which I think was due to impedance mismatch.
This is NOT caused by impedance mismatch. An 8 ohm speaker is a very low impedance, one tiny BC107 will have BIG trouble to drive it. Not at low volumes but at even a moderate volume, a BC107 wil not cut it. What happens when the BC107 reaches its limits ? I starts to clip meaning it cannot provide more signal to the speaker. This clipping you will hear as distortion.

Concerning impedance mismatch: You do not need impedance matching to drive a speaker. 99.99% of audio amplifiers have a very low output impedance. When loaded with an 8 ohm load that means there is actually a large impedance mismatch ! But that is OK since what we want is to put a voltage across the speaker. You usually only need impedance matching for high-frequency signals like more than 10 MHz or so OR for transporting audio signals over long a distance (phonelines).

Now you have oscillations and I think that is because you increased the gain of your amplifier (since you added an extra stage). I hope you agree that the base of Q1 is the input of your amplifier. Note how the voltage at this input is just a divided down version of the supply voltage. If the supply voltage varies, the voltage at the input will also vary !

Now if there is a signal going to the speaker, the second stage draws current. I guess you're feeding this amplifier with a battery so the supply voltage will drop a little when there is current being drawn. This small drop in supply voltage will also appear at the input and it will be amplified and fed to the speaker. Then the speaker will draw some current. See the there is a loop here ? For an oscillator you need a loop. You build one.

I suggest to decrease the gain, you can do that not by changing the value of Cb but by placing a resistor in series with Cb. A value of 180 ohms is a good starting point.