Well, for all of your synths you'll want the MIDI going into the MidiSport, but you'll also want the audio outs to reach the MBox, so you can actually track the sounds from the synths... as you can't bounce midi. This is where a patchbay is very useful, because it'll allow you to easily switch between what you connect to the mbox. You'll set up your patchbay so that all of the inputs and outputs of your various pieces of outboard gear are connected to the back of it... just remember where everything is patched, labelling the patchbay is a VERY good idea... Keeping your midisport and your patchbay separate.
Once you have everything set up, you might have played a midi part into Logic, that you want to run through the triton. So using your midi ports in logic on the general midi track, you'll enable the triton. You'll then patch the triton's output into the mbox input. For example: Triton output L into mbox input 1, Triton output R into Mbox input 2. Then in Logic, either make 2 mono audio tracks (one set to input 1, the other set to input 2), or one stereo audio (input 1-2); making sure you're running your audio through the mbox, in your i/o settings. Once you've done this; record arm your midi track, and your audio tracks, hit record, and let logic play through. The midi information will be sent to the triton, which will put it out as audio, which then gets recorded back into logic... I hope I've made this easy to follow.
If you want to use your compressor on something: make the logic audio track's output 'output 1', then on the patchbay, patch mbox output 1, into compressor input; then from compressor output 1, into mbox input 1. Create a new audio track in Logic, with the input set to 1, and the output set to the stereo out. then record that track.
Also, the axiom and artist mix don't need to be connected to the patchbay, they are fine going through usb and ethernet... of course you could connect the axiom to the midisport if you wanted, but once it's all set up, you can actually use the triton as a midi controller.