Reducing noise in this audio amplifier
It depends what sort of noise you're talking about. I suspect, given the configuration of Q3, that you're getting a very distorted output because Q3 is not biased to work in its linear region.

Imagine something like a 2V p-p sinewave coming through C4. Q3 won't begin to conduct until that signal goes above 0.6V or so, and it won't conduct at all below that - including throughout the negative half of the cycle. What you'll end up with going into your headphones is a sort of square wave with a round top - a massively distorted version of your original signal. The base of Q3 would need to be biased to at least 1.6V in order to achieve the desired output. Obviously that will introduce a DC component to the output, so as stated in the comments you will need a coupling capacitor in series with your headphones to remove that.

You might want to consider a push-pull output stage - read up on class AB amplifiers. You might also want to investigate some of the free online circuit simulators: you can feed your circuit with a test waveform and look at points around it with a virtual oscilloscope. It'll become painfully obvious where the problems lie.