Sometimes, I think pop culture helps us relate far better to the ancient writings than any in-depth discussion ever could. Of course, I would encourage one of those discussions after getting the basics from pop culture, but the point here is: pop culture does one thing very well: filter out the basics. I've been reading the Odysseia again, as a homage to Athena for the Panathenaia and while looking something up, I stumbled upon the versions of the Iliad and the Odysseia. From Wikipedia:

"TV Tropes, also known as Television Tropes and Idioms, is a wiki that collects and expands on various conventions and devices (tropes) found within creative works. Since its establishment in 2004, the site has gone from covering only television and film tropes to also covering those in a number of other media such as literature, comics, video games, and even things such as advertisements and toys. It is known for approaching topics in a casual and humorous tone—cyberpunk author Bruce Sterling once described its style as a "wry fanfic analysis.""

I love TVTropes, and browse there regularly. I just never realized they had also taken on the Iliad and Odysseia. One thing TVTropes does very well is remove the grey and ambiguous; they put labels on everything and give a reason for that. I know some people will find this incredibly annoying, because a lot of nuance is lost, but it also brings to the foreground a couple of points you might otherwise have missed. I'll give you a few examples for both tomes and then you decide: useful or not?

The Iliad
  • Anti-Hero: At the time of the tale's origin, Achilles was definitely not an antihero, but due to Values Dissonance, many readers see Achilles as a colossal Jerk Ass and are more sympathetic to Hector, who is not a nice guy either.
  • Armor Is Useless: Played with. Oddly enough, whether a warrior's armor protects him or not depends on how much Plot Armor he has; in a sense, the real armor is used as a Handwave for Plot Armor. At any rate, this is a Defied Trope in-universe, considering that every time a warrior dies there is a fight over who gets to keep the armor.
  • Big Brother Instinct: Agamemnon to Menelaus. Seriously, don't hurt his little brother.
  • Bond One-Liner: After spearing Cebriones and causing him to backflip out of his chariot, Patroclus remarks that he'd make a good oyster diver. Of course, this being The Iliad, it's a bit longer than one line.
  • Did You Just Flip Off Cthulhu?: Early on, Helen gives Aphrodite a piece of her mind. Aphrodite puts her in her place shortly afterward, but damn, girl!
  • Due to the Dead: Proper respect towards corpses is very, very, very important in The Iliad. Fights over corpses are common, with the fallen man's allies striving to give the corpse a proper burial and the enemy wanting to desecrate it. There are also occasional truces to allow both sides to recover their dead.
  • Good Cop/Bad Cop: Odysseus and Diomedes were on a night raid and captured the hapless but useful Dolon. Bad cop Diomedes said to stand still or die. Good cop Odysseus said, "Fear not, let no thought of death be in your mind." It went on like that for awhile until Diomedes "struck him in the middle of his neck with his sword and cut through both sinews so that his head fell rolling in the dust while he was yet speaking."
  • Loads and Loads of Characters: And roughly 70% of them get killed off.
  • Sacred Hospitality: One of the more famous examples in literature. Paris steals Helen while he's a guest in her and Menelaus' home. While the act has plenty of political ramifications, it's the breach of hospitality that causes such an uproar, and is used to rouse the entire army of Greece to sack Troy in response.
  • Shipper on Deck: Agamemnon becomes exponentially funnier if you view him as a Helen/Menelaus shipper. It's not even inaccurate.
  • We Are As Mayflies: Homer returns to this idea repeatedly, expressing it through a metaphor likening human beings to leaves as autumn approaches.
  • What Happened to the Mouse?: Aeneas. Just as Achilles is about to kill him, the Gods save his life and declare that after the war, he shall be the leader of all future Trojans. He's rarely mentioned again, and then only in passing. 800 years later, Virgil decided to make this a Brick Joke.
  • Why Don't You Just Shoot Him?: The Trojans could have just given Helen back to avoid total annihilation, but this would have gone completely against Greek culture, and certainly would have made a lousy story. The Trojans are actually ready to do this after Menelaus beats Paris in their duel, but an archer on the Trojan side shoots at Menelaus during the intervening truce, restarting the war.
The Odysseia
  • Accidental Pornomancer: On his way home, Odysseus spends years as the bedmate of two beautiful women: the Hot Witch, Circe, and the sea nymph, Calypso. Neither options were by choice, and Odysseus is typically justified in that he never stopped loving or wishing to return to his wife.
  • Bolt of Divine Retribution: Athena threatens one of these in the last book when Odysseus tries to go to war again.
  • Brains: Evil; Brawn: Good: While Greeks valued Odysseus' cleverness, the rigid he-men Romans hated his deceitfulness and portrayed him much less sympathetically. It helps that he fought against the Trojans, whom Romans believed were forerunners to their own culture.
  • Hachiko: Odysseus' dog predates the trope namer, waiting faithfully for his master before dying shortly after his return. In some interpretations he dies happy, but according to Homer Odysseus is forced to pretend he doesn't know the dog, making this a Tear Jerker.
  • Happiness in Slavery: As described in the epic, slaves and masters were not as far apart as in other ages, for instance the swineherd Eumaios was raised by Odysseus' mother Anticleia almost like a son alongside her daughter Ktimene, and became wealthy enough to buy a slave of his own. And Menelaos makes Megapenthes, his son by a slave, his heir.
  • I Am A Humanitarian: Not only Polyphemus, but also the Lestrigonian, who ate several of Odysseus crewmembers.
  • Impossibly Delicious Food: We know, we know, never refuse free food, but it's probably not a good idea to accept handouts from the Lotus-Eaters.
  • Nice Job Breaking It, Hero: Odysseus and his remaining crew escape from the cyclops, when Odysseus has a fit of hubris and mocks the injured cyclops along with revealing his true identity. Sure, the mountaintop that is thrown at the ship misses. The raging storms, however, do not.
  • Random Events Plot: Odysseus' actual voyage, which is the most famous part of the story. By contrast, the parts about Ithaca, Telemachus, the suitors, etc. have a normal plotline to them.
  • Rocks Fall, Everyone Dies: Helios sics Zeus on your ass, lightning falls, everyone dies.
  • The Thing That Would Not Leave: The suitors, for three years at least.
  • Who's on First?: Possibly the oldest example in the book. Odysseus told Polyphemus his name was "Nobody" (μη τις). When the Cyclops started screaming that he had been blinded, his brothers asked who had done this foul deed. The Cyclops replied that "Nobody has blinded me", so his brothers told him to shut up with the screaming over things that hadn't happened. As an added bit of wordplay, μητις (one word) meant "cunning" in Ancient Greek.
  • You Can't Fight Fate: What we would call an Overused Running Gag.