Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Serious
In keeping with its focus on matters of life, death, fate, and the relationship between mortals and gods, the Iliad maintains an elevated or lofty tone. How lofty? So lofty:
(Achilleus:) […] afterwards when the sun sets
make ready a great dinner, when we have paid off our defilement.
But before this, for me at least, neither drink nor food shall
go down my very throat, since my companion has perished
and lies inside my shelter torn about with the cutting
bronze, and turned against the forecourt while my companions
mourn about him. (19.208-213)
Yikes. SAT words, grand phrases, proclamations a'plenty... the only way this could get more elevated is if it were literally on top of the Burj Khalifa.
This is not to say that the Iliad is entirely without humor. The chattering and petty rivalries of the gods are clearly played for comic effect, as are some of the speeches and actions of the mortal characters. All the same, a serious tone is definitely the baseline, and lighter moments play off that.