PCB layouts like that don't work at high frequencies. The tracks work as inductors (think of them like a coil that has been un-wound) and as the frequency increases the amount of effect they have on the circuit becomes significant. You also have a problem with the orientation of the two coils, when they are close to each other and aligned the same way, they will magnetically couple to each other and the last transistor (feeding the antenna) may become an oscillator in it's own right instead of only being an amplifier.
Start your layout with a 'ground plane', make as much of the area as possible into copper ground. Most PCB packages have a facility to 'copper pour' or 'food fill' so all the available space is filled with copper and connected to one node, groud in your case. That does two things, it makes sure the best possible ground is available and it also provides a degree of screening from outside influences.
Also orientate the two coils at 90 degrees to each other, either rotated on the board surface or with one having its axis up and down, in other words you can look through it's middle to the board underneath it. That will reduce the amount of signal coupling between them and help to keep the circuit stable.
I would also move the capacitor across the battery to the other side so it is closer to the circuit. It's purpose is to ensure there is no signal on the supply line but at the moment you have the length of the tracks between the capacitor and the critical circuit that needs to have a clean supply.
If the frequency is tuning correctly but the microphone is insensitive, something is wrong around the first stage. Have you got the microphone the right way around? If you have a voltmeter, measure the voltage across the microphone and at each side of the 1M resistor with the meter negative probe to the negative side of the battery. I suspect the 22K resistor feeding the microphone may be too high in value when only using a 3V supply for it.
Brian.