The unconscious sublime
The book is like a fever dream. The randomness of the book is only feigned; in reality, the wildly dissociative symbols and scenes culminate into a beautiful portrait of what lies beyond the realm of consciousness. The book is written in pseudo-language, because language is the realm of consciousness, one might say, so to write the book in a new tongue verging on absolute chaos puts the reader into the deciphering role. Not only do they have to understand the sublime symbolism (which is deeply archetypal and metaphysical), but they have to do so by approaching the novel through a field of chaos. Before someone can read Finnegan's Wake, they have to learn a new language, the language of only this novel sui generis.
Family dynamics
There are basically three central families in the text, but the first and last are minor so that the major family is the Earwicker family living in a suburb of Dublin. The first family is Finnegan's family: Finnegan is a raging alcoholic who literally resurrects himself from the dead to get one final whiskey; his wife serves his body at his own wake (one dynamic is portrayed). Then, the final family is the Porter family whose parents just want to make love, but their children keep interrupting with nightmares (another dynamic). Lodged in between those is the Earwicker family. Rumor has it the father has molested some young girls while drunk in the park, a statement on his predatory quality; the mother uses language to recast him in their community, and she has the first and last say in the novel, so that she is something like a "great mother" figure. The sons are in Oedipal competition, so that they are like Cain and Abel, and Issy is the spoiled baby who is in Mommy's pocket the whole time.
Religion and reality
The central thematic argument of Joyce is not chaos! Although the book is a post modern masterpiece, its central argument is not that there is no meaning whatsoever, but rather, that there is obvious meaning, but only for those who are patient enough to see it. If the reader patiently attempts acquiring Joyce's made-up pigeon Gaelic-English, they will see a religious portrait of psychological archetypes emerging from the mayhem of language; they will see Adam and Eve, in cahoots about a divine sin (in this case, their forbidden fruit is pedophilia); they will see Cain and Abel competing for Mommy's love; they will see the Mother-Daughter complex between ALP and Issy. Also, the novel starts with an undeniable religious motif. Finnegan is a dead man who resurrects and whose body is offered at his own wake, signifying the resurrection and Communion of the Christ. The book ends with a Hindu symbol because the "great mother," ALP turns into a river and runs away into the lowest parts of the world, like the great river.