This is a very interesting question. Of course, postmodernism and its characteristics in literature are notoriously difficult to define, and yet we are able to pinpoint a few general characteristics. Above all, the clearest link we can establish between postmodernism and this collection of war time stories is the way that Tim O'Brien deliberately plays with the concept of truth, presenting us with stories that, he later goes on to admit, are not actually true. We can helpfully link this to the postmodern concept of metafiction, in which authors deliberately draw attention to the artificiality of their work.
It appears that above all O'Brien is trying to make his audience confront the artificiality of his portrayl, and in particular struggle with the key concepts of fact and fiction and the importance of these terms. He famously said once during a conference of literature during the Vietnam war that "A good story has a power... that transcends thequestion of factuality or actuality." Famously, he believes that telling stories can save our lives, and the final story of this collection, "The Lives of the Dead," presents this view with its opening sentence:
But this too is true, stories can save us.
If there is one story that deliberately presents the confusing relationship between fact and fiction, however, look no further than "How to Tell a True War Story," where at the end, the narrator admits that the story he has just told was not true as he struggles to convey the experience of war:
Beginning to end, you tell her, it's all made up. Every goddamn detail--the mountains and the river and espeically that poor dumb baby buffalo. None of it happeneds. None of it.
O'Brien seems to be reaching beyond such artificial distinctions as truth and fabrication to focus on the way that good stories contain a force or a power regardless of their status as fact or fiction.