While both the short stories "My First Job" and "The Election" found in Lynda Barry's One Hundred Demons are inaccessible online, we can certainly give you general advice about exactly what demons are in these stories and how to find them. In general, the demons actually represent the main themes in the stories. A theme is an underlying concept or a repeated idea within a piece of literature. A theme is not necessarily a moral, but it certainly can be. In general, a theme is a universal idea that the author is trying to convey and make a point about. For example, common themes we see in Charles Dickens would be the effects of poverty, child abuse, and social injustice. Just like Charles Dickens and other authors, Lyda Barry has used the concept of demons to create themes and assert main points. It's also important to note that a demon can be defined as something that continues to have a mischievous or negative influence on a person's life. For example, one person's demon could be alcohol. Hence, the ongoing theme you are looking for that can be characterized as the demon in the story is the theme that has most negatively influenced the character in the story. Let's look at the story titled "Head Lice" as an example.
This story is about a girl who grew up feeling like a social outcast; her feelings of rejection even continued in her adult life. Head lice is certainly a recurring motif within the short story, but the central themes are really more about loneliness, inferiority, rejection, and acceptance. The girl was rejected in elementary school, mostly because she had red hair. Her loneliness then caused her to develop an obsession with bugs, and her conversations about bugs incited those around her to reject her even more. It was not until she vacationed in the Philippines that she finally learned the feeling of being accepted. She met friends in the Philippines who seemed just as eccentric as she was and who even obsessed over head lice yet were still popular. She developed her first crush on a boy who was was very popular and very intelligent, even liking bugs just like her, as we see in Barry's passage:
I was falling in love with the kid everyone called The Professor. He was the smartest kid I ever met and he liked bugs.
However, the friends she developed in the Philippines made her feel even more lonely, rejected, and inferior once back in the states. As an adult, she finds her first boyfriend, but he is so arrogant and condescending that he is really just a new form of the same old rejection she had to face as a child. Hence, we see that it is really her own sense of inferiority spurned by others' rejection of her that is really continuing to create the rejection she has to deal with in her life. Therefore, the real demon in this story, which is also the dominant theme, is inferiority.
We can see from this that what you are looking for in your own two stories is the ongoing theme that also creates the problems for the characters, and this ongoing theme will also be the characters' demons.