Monogatari uses the occult in a variety of different ways: to represent mental illness, to explore past traumas, sometimes even as a simple plot device; I believe that this variety is part of what makes Monogatari such a great series, even including the plot devices, but what speaks to me the most is when Monogatari uses the occult as a vehicle for self-contradiction.
Hanekawa Tsubasa is a near perfect example of this; at the outset, she appears to be a flawlessly good person, one that could be compared with the Kantian ethics of always doing only what is rationally good. However, to accomplish this, Hanekawa has to shed her own emotions and do everything out of an apathetic common sense. Humans aren’t purely rational beings, and acting this way causes her parents to see her as a monster and causes her own shunned emotions to manifest as various cat monsters.
At this point, she is more comparable to Maria Von Herbert, who wrote a letter to Kant pleading for help, that as a result of following his moral law, she had been swallowed by despair and apathy, and who ultimately commited suicide when Kant brushed her off. It is only by accepting her emotions that Hanekawa avoids a similar fate.
Even Kaiki Deishuu, who readily admits to being a con artist who does everything out of personal benefit, contradicts his own philosophy twice in Koimonogatari. First, he decides to help an old flame, rationalizing that it is still to his personal benefit. Second, the entire arc, so SPOILERS AHEAD.
Throughout Koimonogatari, Kaiki gathers more and more information about Sengoku Nadeko’s relationships with others and her hobbies, which he considers utterly useless for the purpose of deceiving her. However, he ultimately fails to deceive her because he fails to understand that Nadeko doesn’t particularly trust anyone.
Kaiki is forced into a situation where the only way to save himself is to give Nadeko life advice, helping her realize that clinging to her love for Araragi denies her ability to understand and direct herself. In the end, he encourages her to pursue her own dreams with the money he’s given her over the course of the month, a strong irony given his own self-evaluation as a cynical con artist.
There are other examples throughout the series as well, and I would actually say that the idea of the Shadow, a la Carl Jung, is quite prevalent in Monogatari. The reason I pointed out these two in particular is because whereas many of the other characters more or less struggle to live as an ideal Persona with violently destructive Shadows like Hanekawa, Kaiki by contrast, puts on an extremely cynical and self-interested Persona with an ultimately sentimental Shadow. (Meanwhile, Tsukihi has no Shadow or Persona, which is fine too, I suppose.)
Fundamentally, the occult is a play on the visible and invisible, and the way Monogatari introduces the occult is through wordplay, where Japanese characters can be read at face value but also carry deeper attachments to their past. Not every instance of this results in self-contradiction, but if that’s not a metaphor, then it’s a double entente.