I use a Mac so I'm not sure how well this translates to Windows.
For the first year or so, all I used was a shareware recording program called'SoundHandle' I plugged the guitar into my effects pedal, took the output from that and used a 1/4" to 1/8" adapter to plug it into the mic input on the computer. Then I set the audio control panel to record from the mic input and recorded as a .wav file.
After that you convert the .wav file to MP3 using a shareware conversion utility like N2Mp3.

I use Cubase recording software now, but the recording setup is essentially the same.

ie, Guitar to MultiEffects Pedal (with a cabinet simulator)
MultiEffects Pedal to Mixer
Mixer to Mic input (using a 1/4" to 1/8" adapter)

Not sure why you'd be getting distortion except maybe you're trying to use a mic and overloading the input