I've been studying Japanese for a bit now and had to look up the the reference to squid in Monika's name. Natsuki breaks down Monika's name into Mon and Ika. If you do a google translate, you'll see that squid translates into the characters 'i' & 'ka' (い & か). Therefor you have Ika (いか) for squid as Natsuki (な na, つ tsu, き ki) tries to play out. Monika kind of breaks the forth wall a bit in this by explaning that it doens't work in translation, Mo-ni-ka, as we would say her name in English. Actually, it would be roughly the same in Japanese as well, もにか (も mo, に ni, か ka) but Natsuki breaks the ni down into seperate characters (ん n & い i) for Mon-ika (もん & いか).
... hopefully that wasn't too confusing.