Yobisute (no honorifics) at the end of Monogatari Series Second Season Episode 24 At the end of the episode Kaiki doesn't use any honorifics...


   ...when speaking with Hanekawa.


This is highly unusual since they have never spoken with each other before. What is the significance of him deciding to use yobisute?
I don't think there's anything unusual about it. You're right that in real life, omitting honorific suffixes (i.e. yobisute) when first meeting someone would be unusual, and may even be considered downright rude. When it comes to anime characters, on the other hand, that just isn't so. Characters will often refer to others in ways that would be considered inappropriate in real life.1
Kaiki, in particular, never uses honorifics, except for senpai for Gaen Izuko (and that, too, is inconsistent). Consider the first time Kaiki refers to Karen by name (in episode 5 of Nisemonogatari; also their first meeting):

KAIKI: どうした？震えているぞ、阿良々木。
KAIKI: What's the matter? You're shaking, Araragi. [no honorific]

And later, when Kaiki first refers to Koyomi by name (in episode 7 of Nisemonogatari; only their second meeting):

KAIKI: …あの元気のいいお嬢さん、お前の妹のことなら、心配することはない、阿良々木。
KAIKI: ...As for that lively girl, your sister - you needn't worry, Araragi. [no honorific]

All said and done, Kaiki's failure to use honorifics when addressing Hanekawa doesn't really mean anything. That's just how Kaiki speaks, and more generally speaking, is how a lot of anime characters speak.

Notes
1 This is why people who learn how to speak Japanese by watching anime often have a skewed sense of what is considered polite in Japanese society - anime characters are often pretty darned rude by real-life standards. This question on Japanese.SE has a bit to say on that topic.