These are some terms that are frequently used in Kodocha (or that I use in the site without explaining). If you have any terms you think should be added, please let me know.
Aoki Award
Mama is the winner of this award for her book titled "The Gigolo and I" (about her and her ex-husband, Ryosuke). The award is the Japanese equivalent of the Pulitzer Prize for Literature.
Buruccha
The toy Sana gives to Hayama to communicate (Rei-kun has one too). It shakes pretty violently when you call someone ^_^; ("buruburu" means trembling).
Human weight doll (hito no omosa/weight of a person)
One of Mama's expensive mail catalogue purchases. It serves as a testing dummy (like when Sana is going to bungee jump) and as something to amuse or frighten people.
"Kirai ja nai"
This is a key phrase in KNO and also the title of this site. It means "I don't hate/dislike you" or "I don't hate it".
To an extent, I'd say it's not uncommon to say this when you say you like something/don't dislike it. But Hayama says this even about things he feels very strongly about, like Sushi. Or Sana...
Komawari
The theater group/acting academy both Mama and Sana attended as children. When Sana was about five, Mama convinced her to join so she could be "just a bit more famous than other children" to make it easier to locate Sana's birth mom. Komawari seems to teach all sorts of random things, like special fighting skills ("Komawari kick!") and… croquet techniques…
Kurata-ya
This is the name of the Kurata family's hot springs. They're run by Misako's mother, Kurata Shizuka. She hopes that one day her daughter (or Sana) will take over the business, but it doesn't seem like that's going to happen. By the way, this is a bad explanation, but "ya" means "store" or "shop." For example, bookstore is hon-ya (hon means book). Adding "ya" to the family name is a common way of naming a family business.
Manga
Japanese comics/graphic novels. A lot of anime originates from manga. If a manga series is very successful, it's usually animated. Some series are done in manga and anime form simultaneously, and sometimes the manga is made after the anime.
Manga-ka
(professional) manga writer/artist, like Miho Obana.
Nori-nori machine
Sana's little rapping machine. It plays music and does remixes. ^_^
OVA/OAV
"Original Animation Video." These are series released to video only. They can be very short (like the Kodocha OVA) or as long as a TV series (Record of Lodoss War).
Oyakodon-baka
This is a great "term" Sana uses to refer to Hayama's family at the beginning of the series (when she's upset over how they act toward Hayama). A most people know, "baka" means "idiot." Oyako-donburi (oyako-don), on the other hand, is a dish that consists of rice topped with chicken sort of scrambled with eggs (prepared with a kind of soup stock). "Oyako" means "parent and child" (oya=parent, ko=child), and the dish is obviously named that way because the chicken is the parent, and the egg is the child (^^;). So with "oyakodon-baka," Sana is calling them a "stupid family" in a very creative and demented way. Would you expect any less?
Peggy Hayama
Peggy Hayama is a singer. Sana randomly calls Akito "Peggy" to his utter confusion ("Dare ga Peggy da… ").
Sensei
I guess this literally means "person who guides/leads" (
=sen=preceeding, 
=sei=person) or someone who is born before you, has lived more, and therefore knows and has done more (sen=before/ahead sei=person/life/birth). I really hope that was more illustrative than confusing…
Anyway, "Sensei" is the word used for "teacher," "professor," or "master," and it's a term you also use to address professionals/people of higher education/social status (doctors, politicians, lawyers). Mama is a well-respected writer, so she's addressed as "sensei" by Rei, Shimura, and Onda. Since it's a term of respect, you wouldn't use it to describe yourself.
Shoujo
The Japanese word for girl/girls. Shoujo anime and manga are just series that are geared/marketed towards girls. They include many different types of series and have different sub-genres. Some examples of Shoujo manga/anime: X, Fushigi Yuugi, Kakumei Shoujo Utena, Cardcaptor Sakura, Basara, and Vampire Princess Miyu.
Tankoubon
Manga series that run in magazines are later compiled into tankoubon, with several chapters per book. They usually have a soft cover and a glossy dust jacket. Mmm...
