To being to explain the oxymoron used in Wilfred Owen's poem, "Dulce et Decorum Est," one must be able to define and understand what an oxymoron is.

An oxymoron is (according to eNotes' "Guide to Literary Terms")

a figure of speech in which two contradictory words or phrases are combined to produce a rhetorical effect by means of a concise paradox.

That said, the definition includes another word which needs explanation: paradox. A paradox (again taken from eNotes) is

a statement that is apparently self-contradictory or absurd but really contains a possible truth.

Essentially, an oxymoron is a phrase used to illuminate the fact that two very different, or contradictory things/ideas, can exist.

In regards to the existence of an oxymoron within the first stanza of the poem, the following line depicts the oxymoron.

Men marched asleep.

Readers are very aware that it, under normal circumstances, is impossible to march while asleep. Marching takes a specific rhythm, which needs to be through a conscious effort. That said, when asleep, a person's conscious is shut down--the subconscious has taken over. Therefore, it would seem impossible to march while asleep.

Unfortunately, men at war tend to simply "go through the paces." Their movements become unconscious, given they have repeated them so many times that they can perform them "with their eyes closed." Therefore, although the image of men marching while asleep seems impossible, it can be (and has been) done.