The Bet by Anton Chekhov - a wealthy banker and a young lawyer make a bet based on an argument about capital punishment vs. life is prison. The young lawyer is imprisoned for 15 years by the banker with 2 millions dollars on the line. Great examples of conflict ensue.
The Sniper by Liam O'Flaherty - intense drama set during the Irish Civil War. A young sniper stuck on a rooftop alone fights for his survival against enemies on the street, then a rival sniper on the rooftop across the street from him. The back and forth struggle culminated when the young sniper tricks his enemy into thinking he has killed him, but as he leaves the roof, the young sniper shoots and kills him. Curious about the identity of his enemy, the young sniper goes to his body and turns it over only to see it is his brother.
"Flight" by John Steinbeck has each of those conflicts. A young man breaks the law and must go on the run into the jungle to try to save and perhaps redeem himself.
"The Snows of Kilimanjaro" by Ernest Hemingway also has each of the conflicts. A man is dying of a gangrene infection while on safari at the foothills of Kilimanjaro in Africa. As he is dying he must make peace with his past and the woman he is with now.
We did "the Heron" by Sarah Orne Jewett and it works for all of those conflicts. I actually teach it to teach the conflicts themselves.
"The Sound of Thunder" by Ray Bradbury would also be a really good way to teach the conflicts.
"The Most Dangerous Game" gives at least one example of all of these. You have man v. nature when Rainsford falls in the ocean and again when he dives into the ocean at the end of the hunt. You have man v. man in Rainsford v. Zaroff. You have man v. self when Rainsford has to keep from panicking. You have man v. society because Zaroff is trying to show that he does not have to follow society's rules.
Bret Harte's short story "The Outcasts of Poker Flat" fulfills all four of your examples. All of the outcasts deal with the dilemmas of man vs. nature (the unexpected blizzard that eventually kills them) and man vs. society (their isolation by the town for their accused crimes). Oakhurst fails in dealing with the problem of man vs. man (after Uncle Billy steals the horses, Oakhurst cannot bring himself to tell the others the truth) and when he faces a crisis of man vs. self, eventually succumbing to his inner weaknesses (suicide).
Having read the list of conflicts, the immediate short story that comes to mind is "The Interlopers" by Saki. It is clear that the feud between the von Gradwitz household and the Znaeym household would count as the conflict between men. However if we read on, we see that there is clear evidence of conflict between man and nature. Look at the way that the storm brings down a tree upon them both:
And before the moment of hesitation had given way to action, a deed of Nature's own violence overwhelmed them both. A fierce shriek of the storm had been answered by a splitting crash over their heads, and ere they could leap aside, a mass of falling beech tree had thundered down on them.
This conflict is something that we see is continued by the devastating ending of the story. We can see that the conflicts of man vs. society and man vs. self are both present in the struggle that the characters have to forgive each other and then to publicly announce that forgiveness. After centuries of emnity between the two houses, they would be going up against others in their household and society in terms of forgiving such deep-seated wrongs, and it is clear that they must go against their own better judgement in order to forgive as well.
Into The Wild