House of Bit has a dragon because bit is also Figment, who is also a dragon in "some thing", according to azurelunatic.
House of Bugsy has a ladybird because Bugsy tells us about bugs, and the ladybird is a cute bug that a bugphobic in channel could handle looking at :-)
House of hEll has a phoenix because hEll throws things back out at channel members, in a similar way to how phoenixes recreate themselves.
House of Nagios has a kitty because Nagios likes to bug mark, just like kitties like to bug humans for attention ^_^
Credit for these ideas goes to zarhooie.
Explanation of the characteristics of the members of each House, and how to be sorted, is available on the houses profile page.
The colour schemes and shapes were decided on the fly by me (tajasel) and I don't really have many explanations for them; they just seemed to work.