I take it from your comment that the app you downloaded to use with the computer sound card doesn’t provide the means to demodulate CW, FSK, or SSB signals. Seems like a major shortcoming considering it’s intended purpose was specifically for reception of a CW signal.
The SAQrx.exe is a great app and includes the USB mode and selectable bandwidth filtering. It's ideal for listening to SAQ, but that means for only a few minutes twice a year and it's top frequency is 22kHz. That's fine for tuning in 17.2 kHz, but somewhat limited for exploring higher VLF frequencies.
SAQrx v9.8 can be downloaded here:
http://dl1dbc.net/SAQ/SAQrx/SAQrx_0-98.zipInstant listening on a European Web SDR makes things as simple as possible:
http://websdr.ewi.utwente.nl:8901/?tune=17.20cwThe RSP1A SDR tunes down to 1 kHz (!) and offers lots of mode and filtering choices. That's what I used for testing audio transformers, and the spectrum display and signal level metering helped tremendously in the comparisons of the various transformers.
You bring up a good point about signal levels. The audio oscillator injection point should be at a higher level compared to the antenna input. Most op amps are dual section so theoretically one half could be used for antenna input amplification with transformer isolation/filter/matching and the second half for unity gain mixing. The output would then be line level for driving an audio amplifier. The downside is the lack of bandwidth control so I imagine it would be a lot like tuning in CW using a direct conversion receiver (like the HW-7 I had!).