The jack sockets of the cards breakout box are mono and balanced. They are line level and not intended to drive headphones directly, although they may have amplifiers capable of doing so to some degree, they are not designed for it. You really should use a headphone amplifer.
Although they are mono jacks, the computer sees them as left and right channels of a stereo pair, 1/2, 3/4 etc.
If you want to have both headphone and monitor speakers, you could use output 3 (left) and 4 (right) for the speakers amplifiers and select Delta 44 out 3/4 as the main stereo output bus in your software (options, device order in CEP multitrack and set 3/4 for use in the Edit view (EV)).
In the soundcards driver control panel, you can set output 1/2 to run off the Monitor Mixer (it won't let you use 3/4 for this). With the headphone amp running off Output 1 (left) and Output 2 (Right). The faders in the Monitor Mix will let you monitor any of the inputs and outputs over the headphones. With the speakers running off 3/4, you will only hear stereo playback of recordings. Assuming you can switch your speakers off, this setup will let you monitor everything over headphones while recording without the speakers getting picked up by the microphone.
In the CEP multitrack, each track has a properties dialog. This lets you decide whether it's a mono or stereo track. If it's mono, pick left or right inputs to suit what you have plugged into the Delta inputs.
1/2 - Left, 1 is the "left" input from jack 1
1/2 - Right, input from jack 2
3/4 - Left, 3 is left input from jack 3
3/4 - Right, input from jack 4
With stereo tracks, the left and right channels match the jack numbering as above.
Once recorded, mono tracks have no left and right and will be panned centre unless you change the panning with the pan control.
