Here is a picture of recording to see what's going on: http://i.imgur.com/K3dxmeO.jpg

Am I doing something wrong?

Other than linking to an amazingly huge and vague image, there's no way you'll get 4 tracks simultaneously on one stereo pair.

Of course, I may have misunderstood. Did I mention the image is vague ?

Try describing - in words - what you're wanting to do.

I want to play all instruments simultaneously but record all channels separately into Cubase.

You can't do it with that mixer, as you only have a stereo out (2-channel) and you have 4 inputs.

You can either record 2 at a time, or look at getting a new audio interface instead which would allow 4 inputs simultaneously (and could also replace your sound card).

If the Yamaha mixer has 4 outputs and the Audigy has 4 inputs (stereo line + stereo auxiliary?), it could be possible, but it would be a less than ideal solution. And I doubt the Audigy will be up to it anyway.

A logical setup would elimininate the mixer altogether and be based on an audio interface with 4 inputs with phantom power (if you end up using mics that require it) and hi-z setting (to plug in guitars directly, although acoustic guitars would surely sound better through a microphone, hence my advice to get 4 inputs with phantom power). Something like this: http://www.alesis.com/io4 (just an example with the specifications mentioned - I know nothing about its quality etc.)

Good luck!

I just need to record 2-3 songs. That's why I don't want to invest into anything expensive. Can you tell me how could I do what I want with the setup I have?

There are only 2 ways : Do it all in one go or in several takes on seperate tracks.

Ask around - maybe someone you know has the necessary equipment. Perhaps they'd even be willing to do the recording for you with their equipment.

I see it's hooked up to the Blue jack, if green is Right and blue is left you could at least get 2 inputs going.

Soundcards cost more per input.

By the picture you'd have to record the lump sum and not really process it afterwards.

I doubt the recording quality of an Audigy 2 SE is significantly better compared to onboard sound.

However, if you use Adobe Audition you can record with both devices at the same time. That's how I did my first 4-track recordings: using two SoundBlasters.

Also instead of using Rec Out you can insert a jack cable halfway into the Insert socket of a channel. Then it will act as a Direct Out, tapping off each channel individually. Check the block diagram weather the insert is located pre or post EQ.

Another workaround: record simultaneously to two computers (two channels each), then import the tracks from one into the other and align them.

How can I record 2 channels simultaneously?

By pressing the red "Record" button on each track you need to record at that time
What DAW / recording software are you most familiar with?

I understand that, but what about my mixer configuration?

If you're "abusing" the Insert jacks as Direct Out's as I suggested, you don't need to worry about the mixer. It will then send the output of the mic preamp to your soundcards, regardless of how the fader is set. The only concern is the channel Trim, but that needs to be set properly anyway.
Got any experience with mixers at all? Who owns this one?