The novel series did already end. (15 volumes + 7 side stories)
I only read 5 volumes so far (/15) so I cannot tell how it ends, but the KKN LN are EXTREMELY different from the anime, I can tell you that. If volume 1 and 2 aren't that far (except that the atmosphere is more heavy in the LN, as they added a lot of funny scenes in the anime like that whole passage with the tour operator or whatever which doesn't exist in the LN, and suppressed lot of harsh infos from the novels), it heavily changes with the third volume ( arc with Odessa, Kyouka's little sister). You then realize that the anime completely altered kyouka's information; that the anime did the same for Shiruku, and not only that, but for Gekka too; that the anime almost didn't care for the character's suffering in that volume, and that final fight was heavily altered to make it watchable even by kids* (it's not supposed to be); and that the main scenario isn't even going the same way.
The anime has been heavily altered to be almost a simple comedy anime whereas the original story is a mix of comedy and of a serious story which seem to have quite a good amount of foreshadowing and secrets behinds it. I'm looking forward to the next volumes as it seems that we'll soon learn lots of shocking truth about Kyouka's body, Raichou and Gekka. We're still in an arc covered by the anime, yet the informations coming at us are like, completely different.
Anyway, the LN is miles better compared to the anime. For the anime, they made the choice to ignore completely anything important for the plot and just focused on the comedy. But so far that main plot seems to be fairly entertaining. I like the balance comedy/serious of the LN. While it's not one of my favorite LN so far, it's enjoyable to read and the plot makes you want to read the next volumes, because starting with the 3rd volume you realize that there has been a lot of lies in the beginning about the Enka prophecy and about enka's children, and that a lot of things don't add up properly.
(*the following illustration is from the end of the third novel and is among the softest parts of that fight)