Use the Multitrack View in Cool Edit. For each track you want to record, you have to select a recording device. So, if you want to record two separate tracks at the same time, you have to select two different recording devices for your two tracks. If you're using Cool Edit 2.0, you select the recording device by clicking on the 'Rec' button to the left of the track. If you're using Cool Edit 1.2, you select the recording device by clicking on the lower of the two little grey buttons beside the volume and pan windows to the left of the track.
But of course, before you do that, you have to set up Cool Edit to recognize the Omni card and its outs and ins. Have you done that?