Yeup.
Just take your guitar cable (I am assuming it is a 1/4th inch jack) and plug it straight into the mic port on the stx.
Next, download your favorite recording software. If you have never messed with recording software before, then I recommend you start with audacity. It's very simple to learn, it's free, and there are tons of ways you can customize it.
When you are in audacity and you want to start playing something, hit the "record" button at the top and play away.
If everything goes well, you should actually be recording your music to your computer as sort of a demo, AND you should be able to hear it through your headphones.
There will be a slight delay, but unless you are super man, you probably will not notice.
I am not sure what you mean by ASIO Control panel.
I owned a asus STX a while ago, and I know that it can play audio by using asio drivers. But I do not remember any ASIO control panel.
Can you take a screen shot of it and show it here?