Why did "odyssey" come to commonly mean "journey" while Iliad didn't come to have any common meaning?
The word Iliad does mean, in English,
A long series of disasters or the like (Greek ἰλιάς κακῶν, Demosthenes); a long story or account.
(Oxford English Dictionary (OED)), so the usage is the same as that of the Odyssey. It is not as common.
Two examples are
1609 Bp. W. Barlow Answer Catholike English-man 359 Her stay brought forth..an Iliad of miseries.
1865 Times 29 Apr. An opportunity of learning a whole Iliad of finance in a comparative nutshell.