To write a literary analysis of short stories, you want to first read the short stories over for content. Especially look for any themes. A theme is a main idea that appears repeatedly throughout one piece of work. A theme will always be a universal concept, like consequences of lack of love or consequences of lack of acceptance. Theme is often easily confused by both subject and moral. A subject is merely a topic that a literary work is about; a theme shows the author's opinion ("Theme"). For example, lack of love may be a subject found within a work, but the work may be trying to express just how devastating a lack of love can be, which would be the theme. A moral, on the hand, would assert a principle by which to follow, such as never allow yourself to neglect your son. Once you have a solid understanding of any themes, you'll next want to review the story for any literary devices the author used, especially literary devices that help illustrate the theme. Many different kinds of literary devices exist and below is a link to a literary terms dictionary to help you with this further, but some common devices to look for can be diction, imagery, symbolism, recurring motifs, characterization, and figurative language, such as metaphors, similes, and personification. If you need to analyze more than one short story, and even compare them, you'll want to look for things they share in common, which may be theme. As access to some of the works you've named is limited, let's look at "Samphire" by Patrick O'Brian and "My Oedipus Complex" by Frank O'Connor as examples. Both short stories actually share the common theme of lack of love.
The story "My Oedipus Complex," just as the title suggests, is about a boy named Larry who is very fond of his mother and becomes jealous of his father the moment his father returns home from the war. But more importantly, while his father had been away at war, Larry had become everything to his mother. He was with her all day, every day, and she was very attentive to him as her only son. However, the moment his father returns home from the war, the mother foolishly starts ignoring her son and devoting all of her attention to her husband. In short, Larry had every reason to feel jealous of his father due to his mother's negligence. Therefore, it can be said that one theme in the story is the consequences of lack of love.
Likewise, in "Samphire," the heroine is very evidently suffering from being bullied and dominated by her husband. The story opens with a description of the very harsh and jagged setting: "Sheer, sheer the white cliff rising, straight up from the sea." The author even characterizes the husband speaking to Molly as sounding rather authoritative, even bossy as he asserts his rightness in spotting the samphire, an edible plant that grows along some coasts, growing on the cliff. The author particularly characterizes the husband's authoritative, bossy, and even arrogant tone when the author italicizes words to emphasize the husband's thoughts concerning his own rightness, as we see in the lines:
It is a clump of samphire, Molly ... Molly, it is samphire, I said it was samphire didn't I?
What's more, the author characterizes the wife as feeling tormented, abused, especially of her being just about to cry, as we see in the line, "The round of her chin was trembling like a child's before it cries." We soon learn that Molly's feelings aren't just because of her husband's arrogance. We also learn that Molly is afraid of heights, but instead of letting Molly just be herself, her husband has been persuading her to climb the cliffs, as he phrases it, "He had had to persuade her and persuade her to come up even the smallest cliff at first"; he further says,"He had to be a little firm." Clearly, the phrases, or diction choices, "persuade her and persuade her" and "be a little firm" are gentle and not very subtle ways of actually saying he bullied her. It is due to the way he bullies her to do what frightens her plus his arrogance that drives her to attempt to push him off the cliff. Hence, through the author's use of italics, imagery, and even diction, we see that one major theme again concerns the consequences of lack of love.