"Then came the war, old sport. It was a great relief, and I tried very hard to die" Why would Gastby say such a thing?!

Perhaps he means to die on a more metaphorical sense. Throughout the progression of his life he was always striving to be someone else - this persona of the american dream however when he went to war perhaps it was a transitionary state where he was "killing" his old identity and creating a new one. Hope this helps!