An oxymoron is when a phrase is constructed using contradictory words or ideas that are placed next to each other. Some examples of this in common speech are the classic "jumbo shrimp" or the overused "deafeningly quiet." Like the previous answer noted, the phrase "A Merry Way" certainly constitutes as an oxymoron; wars aren't merry, they are very sad and horrible! If you need a direct quote for this, it occurs first in act 1, scene 1, said by Leonato.
"You must not, sir, mistake my niece. There is a kind of merry war betwixt Signior Benedick and her: they never meet but there's a skirmish of wit between them."
The oxymoron of the "merry war" between them gives a sense of the playful teasing between the two.
If you need more instances, there is another good one in act 4, scene 1. Claudio says:
"O Hero, what a Hero hadst thou been,
If half thy outward graces had been placed
About thy thoughts and counsels of thy heart!
But fare thee well, most foul, most fair! farewell,
Thou pure impiety and impious purity!"
Impiousness and purity are distinctly opposite ideas, yet they are placed next to each other here. Interestingly, the oxymoron is reversed as well.