Greatwinter Trilogy

Sean McMullen's Greatwinter trilogy. The US titles are Souls in the Great Machine, The Miocene Arrow, and Eyes of the Calculor, and are set in Australia and North America two thousand years after the start of a nuclear winter.

Souls in the Great Machine
The coasts of Australia are no-man's lands blanketed by the mysterious psychic Call which forces all living creatures larger than a certain size, other than birds, to walk inexorably towards the sea. All major religions ban fueled engines and electrical power, the Libris library system is the centralized keeper of knowledge, and long-distance travel is done by wind-trains and galley-trains. An ambitious and aggressive librarian Zarvora duels her way to the top of the Libris system and proceeds to install a human-powered computer in the central library and uses it to essentially take over Australia.

The Miocene Arrow
Almost all of North America is blanketed by the Call, with only a few small areas safe. Religious taboos against engines are interpreted differently here, and duels are fought amongst aristocrats in alcohol-powered lightweight wood-and-paper aircraft. Rebels from Australia, having hijacked ancient airship technology, arrive in North American and begin to subvert the stable society there using human-powered computer technology.

Eyes of the Calculor
Bizarrely concludes the plots and character arcs of the first two books while at the same time introducing the presence of ancient human technology abandoned in orbit of Earth by the dying previous human civilization. While Australians laid ruin to the North American ways of life in the previous book, North American technology proceeds to lay ruin to Australian ways of life in this book.

Provides examples of the following tropes:

 * AI Is a Crapshoot: Averted, though the limitations of non-sentient computers are extremely important.
 * After the End / And Man Grew Proud: References are made to the titular Greatwinter and its aftermath, as well as frequent religious discussion of what translates to global warming and pollution generated by fueled machines.
 * Apocalyptic Log: Explains the titular Greatwinter and allows the main characters to pull off some unexpected genre change.
 * Authority Equals Asskicking: Highliber Cybelene Zarvora.
 * Badass: John Glasken, Highliber Zarvora, Lemorel... in fact, many of the major characters.
 * Badass Bookworm: Highliber Zarvora is a certifiable genius, but achieves her position by killing a number of senior librarians in duels. Also, the entire Librarian Service requires sharpshooting and other combat abilities as part of its rank structure.
 * Chivalrous Pervert: John Glasken.
 * Combat By Champion: How warfare works in North America.
 * Cool Train: Australian transportation is all pre-1800s, except for the long-distance, light-weight galley trains and wind trains - complete with built-in rocket launchers and trainspotter fanboys.
 * Cunning Linguist: Darien vis Babessa is mute, but can read, write, and translate many languages... as long as she can find someone to read her cards.
 * Gambit Pileup
 * Heel Face Revolving Door: Sometimes it's difficult to tell who to root for... or even who's on who's side... or what the sides stand for.
 * Kill Sat: Rains down electromagnetic pulses that make real electronics impossible and human-operated abacus-based computers plausible.
 * Lost Technology: Oodles of it, but specifically electronics, which are not only lost but forbidden by the aforementioned kill sats, fueled engines, which are forbidden by local religious authority, and genetics, which are forbidden but still practiced in a more primitive form by the aviads.
 * Mix and Match Critters: The aviads are humans with avian DNA spliced into their genome, which makes them immune to the Call.
 * Puberty Superpower: Kind of an inversion; up until puberty, aviads are not immune to the Call and have to be placed with human parents to be raised outside of the zone of the permanent Call.
 * Punk Punk: Australian technology is restrained by prohibitions against electricity and fueled engines: thus, inventors have turned towards clockwork, galley slaves, and wind power to create analogs to post-steam technology.
 * Sapient Cetaceans: Scientists reconstruct ancient cetacean DNA and create three members of the species who turn out to be telepathic/smarter than humans. The Cetaceans are, although it's unclear whether they were "civilized" prior to human intervention or not.
 * Took a Level In Badass: John Glasken and his Warrior Monk training. Lemorel Milderellen was already a Badass, having successfully executed a vendetta at a young age, but after her Freak Out she.
 * Unexpected Genre Change: It looks like a Schizo Tech piece of pseudo-historical fiction until you learn that Greatwinter was a nuclear winter, the Mirrorsun is device left over from, and the deit(ies) who smite electrical engines are actually.
 * Vice City: Rochester never experiences the roving Calls that even the interior parts of the Australian continent must endure. Since at least one major religion believes the Call is divine, it is thought that Rochester is a den of iniquity where people lose their moral vigilance. They're kind of right.
 * Your Cheating Heart : Several major plot-points revolve around the infidelity of certain characters, Glasken in particular. A major turning point of history revolves around the cetezoids' use of a researcher's memory of his surrender to a moment of infidelity as a student.