In Tim O'Brien's novel The Things They Carried, what is the effect of O'Brien's movement back and forth from pure story to commentary about stories general?

As your question implies, Tim O'Brien's The Things They Carried is an exercise in relating the truth of the Vietnam War experience and telling the reader how to interpret that truth.  Several literary critics have noted that O'Brien's novel is an example of metafiction, loosely defined as writing that explores the relationship between writing about experience--in this case, war--and telling the truth about that experience in such a way that the reader feels the experience.
O'Brien deftly weaves narrative and commentary on that narrative in order to make the reader understand the difference between literal truth--that is, the actual sequence of events--and how the soldier perceives the sequence of events, which, in O'Brien's view, can be vastly different:

In any war story, but especially a true one, it's difficult to separate what happened from what seemed to happen.  What seems to happen becomes its own happening and has to be told that way ("How To Tell A True War Story").

He illustrates this different "reality" by telling us how Curt Lemon dies and how those who observe  Lemon's death "tend to miss a lot," a situation that creates "that surreal seemingness . . .but which in fact represents the hard and exact truth as it seemed."  In other words, the lens through which soldiers observe the brutality of war creates a picture based on perceptions which, for the observers, become their reality, a reality that may seem completely at odds with the occurrence as it happened in linear time.
This kind of "truth," because it does not reflect what may have actually happened, requires what Samuel Taylor Coleridge (in a much different context) called "the willing suspension of disbelief."  In other words, to understand the truth of a soldier's experience, the reader must be willing to accept the "surreal seemingness" of O'Brien's war story.  
In order, then, for O'Brien to convince us that what seems to happen, as opposed to what actually happens, is a soldier's realty, he must tell us how to understand a "true war story."  Our conventional view tells us that war stories can be moral, uplifting, reflecting the goodness of the human spirit, but O'Brien must convince us instead that 

A true war story is never moral.  It does not instruct, nor encourage virtue, nor suggest models of proper human behavior. . . . If it seems moral, do not believe it.

Without the constant interplay between narrative and O'Brien's instructions about how to interpret that narrative, we cannot understand--because most of us have not been in combat--that for soldiers whose daily life is haunted by brutality and sudden death, reality is perceived, felt, a truly visceral punch to the psyche.