Great question; yes, oxymorons are used in the novel. As has been explained, an oxymoron occurs when two terms contradict each other and yet still make sense. One of the best examples that we use frequently (that is not in To Kill a Mockingbird) is the phrase "jumbo shrimp." Jumbo means large; a shrimp is generally small. Still, we understand the meaning of the combined term: jumbo shrimp are simply shrimp that are larger than average.

Another example is in the phrase "bittersweet," which references something that is both bitter in flavor and sweet in flavor at the same time, such as sugar (sweet) mixed with coffee (bitter). (Bittersweet can also reference a circumstance that is both pleasant and unpleasant at the same time.) The word bittersweet (another example of an oxymoron) is used in To Kill a Mockingbird in chapter 12, when Scout and Jem go to visit Calpurnia's Church. Scout describes the aroma of the place:

The warm bittersweet smell of clean Negro welcomed us as we entered the churchyard—Hearts of Love hairdressing mingled with asafoetida, snuff, Hoyt’s Cologne, Brown’s Mule, peppermint, and lilac talcum.

Another example of an oxymoron in To Kill a Mockingbird occurs in chapter one:

Somehow, it was hotter then: a black dog suffered on a summer’s day; bony mules hitched to Hoover carts flicked flies in the sweltering shade of the live oaks on the square.

Here, as Scout discusses the town of Maycomb, the setting of the story, she explains that it was hot even in the shade. Shade is generally defined as a place of coolness, a place out of the heat of the sunshine. Sweltering generally means very hot; shade is not generally sweltering. The two terms together form an oxymoron to show the extreme heat of Maycomb, Alabama.

I have not been able to find any concrete examples of oxymoron, which is a figure of speech that combines two seemingly incongruous things, such as "jumbo shrimp." There may, however, be some implied oxymorons. One that I can think of for the setting and time of the novel is "racial justice." Would Tom Robinson have been convicted of rape if he had been white?

Another oxymoron might be "fatherly love" as displayed by Bob Ewell. He is a racist and is abusive to his children.

The concepts of Southern hospitality and Christian charity are turned into oxymorons in the novel as well, in the shunning of Boo Radley, the gossiping of the women, the teacher's hypocrisy, and the like.