Michael makes excellent points...

Sunday I was struggling with a simple crystal oscillator I had kludged
up on a protoboard for a quick project... I have been building
oscillators like this on and off for over 40 years, yet I could not
get this one to work... Tried different crystals... Used the LC meter
to check the caps and inductor... Used a VOM to trace the circuit and
measure the resistors... Had the oscilloscope and a receiver
monitoring the circuit for RF... I was just tearing my hair out... My
son got involved and he could not find a problem either...
As we sat there staring at the half dozen components on the protoboard
I commented that the bias voltages on the FET showed that it was
conducting, but not oscillating as if something was sucking the RF to
ground... On a whim I said to him, pull the RF bypass cap off the 5
volt DC line... (the LC meter had showed the cap as good and close to
the 0.1 mfd it was marked)...
Ahh that won't change anything because the RF choke blocks the rf from
getting that far, he said...
Well, just try it..
He reached over and idly plucked the DC bypass cap off the DC input
line and WHAMMO, instant loud, whistle in the receiver and the
oscilloscope showed a solid sinewave...
He looked at me, I looked at him, we both shrugged and he tossed the
cap into the wastebasket...
It's the little things that will drive you to drink...

So, first verify that your oscillator is oscillating - receiver or
oscilloscope or RF probe to your VOM... It is not just some white
noise in the radio, but a solid whistle that indicates the oscillator
is working... As Michael suggested use a second oscillator as a BFO
if your receiver doesn't have a SSB or CW mode...
Next, put an audio signal into the audio amp and verify that it blows
the headphones off your head... Just suck some audio off a receiver
to feed it...
Once you KNOW these items work then try your mixer... Start with the
transistor mixer first...
Building or buying an RF probe for your VOM will be the most versatile
and cost effective tool you can make/buy for these projects..

GL - denny / k8do