Allegory [
https://en.wikipedia.org/wiki/Allegory]:
As a literary device, an allegory is a metaphor whose vehicle may be a character, place or event, representing real-world issues and occurrences. Allegory (in the sense of the practice and use of allegorical devices and works) has occurred widely throughout history in all forms of art, largely because it can readily illustrate or convey complex ideas and concepts in ways that are comprehensible or striking to its viewers, readers, or listeners.
Writers or speakers typically use allegories as literary devices or as rhetorical devices that convey (semi-)hidden meanings through symbolic figures, actions, imagery, or events, which together create the moral, spiritual, or political meaning the author wishes to convey.
[Etc.]
I'm not going to do a complete trip through all of the TOS episodes, but I'll address the episodes listed in the OP.
"A Private Little War" is allegorical of the Vietnam War.
"Let That Be Your Last Battlefield" is allegorical of race-rioting.
"This Side of Paradise" can be interpreted as an allegory of a hippie free love commune where everyone stays stoned and screws all the time but does no work.
I'm not sure I see the allegory in the other two. As I see it, "Who Mourns for Adonais?" is more like a literal critique of the worship of self-interested divine beings than an allegory. I have nothing to say about "I, Mudd" in the context of allegories.
Here are some others:
"A Taste of Armageddon" and "Errand of Mercy" are both allegorical of the Cold War.
"The Apple" is allegorical of the myth of the Garden of Eden.
"The Cloud Minders" is allegorical of social class stratification.
Other episodes are part allegory, part literal representation:
"The Omega Glory" is part allegory of the USA being pitted against the USSR, literally part pro-American patriotic propaganda
"Patterns of Force" is part allegory of the Holocaust, part literal representation of the Nazis.
