Hello -
I just researched your situation thoroughly. It's amazing - the Samsung website and manual don't have enough detail on this monitor to understand what's going on, but luckily newegg had a high resolution image of the back of the monitor so I can see what's up.
The Samsung XL2370-1 has one DVI input and one HDMI input.
It has two outputs for audio, one analog and one digital.
DVI cannot carry audio, but HDMI can. This means that the audio outputs for your monitor only pertain to the HDMI input.
The simplest way to set this up, in my opinion, would be to plug in the XBOX with HDMI and the Mac Mini with DVI (using an HDMI-DVI cable, MiniDisplayport-DVI cable, or any appropriate adapter and a DVI cable).
Then, either:
1 - get two minijack audio cables for the xbox and mac mini and get a stereo minijack splitter, and plug both minijack audio cables into the splitter, and then plug the splitter into speakers of your choice. or
2 - get a set of speakers that have two inputs, and run a minijack audio cable out of the Mac Mini to one input on the speakers, and run a minijack audio cable out of the monitor into another input on the speakers.
I personally would recommend AudioEngine speakers - they're made by a real speaker manufacturer, not a computer accessory maker:
http://audioengineusa.com/Store/Audioengine-2
Also, I should note that your monitor is very limited. It may serve your needs/budget well, but a monitor with TWO HDMI inputs AND audio out, or at least an audio input IN CONJUCTION WITH a DVI input, would be better. A monitor like that would do audio and video switching for you, and you wouldn't need to get an audio splitter or speakers that accept two inputs, because your monitor will switch audio to whatever input you've selected and send the correct signal to the speakers.
A monitor with two HDMI inputs would allow you to plug your XBOX and MacMini in with one HDMI cable each (video+audio in one cable), and then run one audio cable from the monitor to the speakers.
hope this helps!