What is KaijuPunk
It is a basic setting that mixes giant monster/kaiju with the low life dystopian punk world setting.
1. Big Ass Monsters
The Core of KaijuPunk is the existence of giant monsters. These monsters range from indifferent to humanity to actively hostile, and their primary purpose is the destruction of human civilization. While there can be a reason (human predation, anti-pollution, etc) it's not horribly important when the monster is destroying the city and others are converging from various points to attack the currently rampaging.
Most kaiju as not nice, and are as likely to attack each other as to continue their attacks on civilization.
The original kaiju, Godzilla, was a product of radioactive contamination, and where the monster went, he left radioactive fallout in his wake.
The theme of contamination is common in most kaiju films and settings, with the monsters either being the direct product of a man made pollution or waste, or they themselves are a source of toxic emanations themselves. Searching through the ruins of a kaiju attack requires protective gear, not just from the dust and debris, but also from radiation, or chemical and biological agents. Despite the massive size of the monsters, people are just as likely to be killed by this often invisible environmental agent.
The governments and world powers often guide or allow kaiju attacks to support their own political aims and goals. Secret societies know information about summoning and controlling kaiju, but again, only to their interest. The organizations that fight and contain the monsters are large, well funded, and often shrouded in secrecy.
For every negative impact, someone benefits. When tech exporting Japan is damaged, China benefits, when the US is attacked, Russia and other anti-American nations benefit. There is a long term advantage to allowing kaiju to damage and kill in regions that share rival or antagonistic positions.
As already mentioned, there are organizations with the resources, materials, and manpower to fight the kaiju. This ranges from the army, to exotic weapons divisions to mecha strike teams.
The monsters have to be fought. A weak humanity fights back with conventional military hardware and loses until it goes nuclear, or is forced to bait monsters to fight each other. A stronger humanity has fighting robots, slave controlled kaiju of it's own, and exotic weapons that allow them to fight the monsters. The stronger the ability to fight back, the more powerful and common kaiju become.
The presence of giant monsters vindicates, invalidates, and spawns cults and religions. There are people who are going to venerate the kaiju as being divine, agents of the apocalypse, and similar theological musings. In a world desperate and afraid (see giant rampaging monsters) there is fertile soil for strange faith. There are going to be cults, cultural movements, arts, and other things dedicated to the kaiju, and those who fight them. On the up side, this is hero worship of the men, and machines that fight the monsters, and on the down side, it's people who think fighting the monsters is wrong and actively work to undermine efforts to contain or kill them.
6. Criminal Enterprises
It is a common notion that horns represent sexual prowess, which is why rhinos are shot and have their faces chainsawed off. Magnify that with a 120 foot tall monster with horns, people will pay stupid money for kaiju horn, or kaiju bone, or kaiju penis powder, dust, etc in the hope that it will give them longer lasting stronger erections, increase their fertility, decrease their weight, reverse hair loss, or just really get them messed up like no one's business.
With a tightly controlled commodity, the black market for kaiju parts is big business. Black market military goods are also hot, especially with weaponry derived from fighting kaiju, or exploiting kaiju biology.
7. Creative Technology
Technology plays a major part in dystopian lit, as well as the kaiju genre. The creative application of technology should be as a double edged sword, every advantage it gives, there is a cost or penalty to be paid. Giant robots cause massive amounts of collateral damage and are immensely expensive. Exotic weapons have radiation, chemical contamination, unexplored consequences and repercussions. Information technology creates the umbrella of the dystopian world, manipulating and controlling things to the point that no one is really sure what's going on. Is this a good movie, or a news feed. Should I be cheering the destruction, or praying for the people trapped in those toppled buildings?