I'm thoroughly confused. It's sounds as though your service (or the supply) is 240VAC, 3?, 4W. ...which means btw you already have 240/120VAC, 1?, 3W (you just do not use the high leg, i.e the 208V one)... and you are trying to add another transformer that has two secondary windings which can be configured for 240 VAC, 1? primary to 240/120VAC, 1?, 3W or a straight 120VAC output. The X terminals, or in this case "wires" are the secondary connections. As I recall off the top of my head, X1 and X2 are one winding, X3 and X4 are the other. To get 240/120 out, X1 and X4 are your hots and X2 and X3 are connected as the neutral and get bonded to ground. For straight 120, X1 and X3 are connected together, as are X2 and X4. IIRC, the X2-X4 gets bonded to ground as your neutral. The primary should be H1 and H2...
[EDIT ADD]You should verify the winding markings and not connect by what I wrote. After pondering what I wrote, there's a good chance X2 and X3 are the other way... X1 and X3 the terminations for one winding, X2 and X4 the other.[END EDIT]
Anyway, the only purpose I can see offhand for doing this is to achieve perhaps some sort of load balancing on the supply (using A-B or B-C for the primary), or perhaps as a means of isolation...???
As for grounding, you'll have to provide your own means. I have to do the same to a 400KVA transformer on my current project. It's hard to believe a grounding terminal wasn't provided. On top of that, I have two 1/0 EGC's coming in on the supply side and six 1/0 EGC's going out on the load side!!!