Okay, a more serious answer this time.
I'd say the post-lunar rain terrain would be too rough to be passable to wheeled vehicles in many places. (Although the book does mention mech tribes towing wagons behind their mechs.) The total lack of maintained roads wouldn't help, either. I could see a few tanks and other off-road vehicles existing, but they'd be rare pet projects of individual coglayers. Also, in the real world the tracklaying chassis was invented as a solution to trench warfare. Without that impetus, and with mechs already available, caterpillar treads might never be invented.
Airships, well, I can't see how they could survive the lunar rain. Remember that a heavy night can sandblast/burn a leather cloak into uselessness. It'd be really tough to make a gasbag that could take that without constant repair, and folding the bag every night would be hugely impractical. That said, I can imagine very rare and expensive magical/technological solutions to the problem. Hm, how about an alliance of dwarves and elves building an airship with magical protection and using it to challenge the hegemony of the city-mechs with their greater mobility? They'd be immune to the usual raiders, and batteries of javelin racks supported by powerful elven mages could keep the lunar dragons away. A variant Protection From Arrows spell combined with blanket energy resistance would guard against lunar rain and dragon breath. Could be an interesting plot hook.
Now, trains would make a lot of sense. The intro even mentions the dwarves using steam-powered tunnel cars long before the lunar rain, so I can definitely see them having a large network at this point. I could see a dwarven initiative to build surface (or shallow-tunnel) rail lines as well, to facilitate long-range trade. This could produce plenty of adventure, too: guarding the construction workers, patrolling the line for breaks, foiling (or assisting) sabotage attempts from jealous mech traders...