I would not recommend using either in speech nor in writing. Not in speech because the risk of mispronouncing either "apud" or "chez" is greater for a non-native speaker. Not in writing because apud (which I have never come across) is too formal and obscure you risk coming across as a snob, or someone who was using it as their "word of the day" Using chez to say something or someone is at someone's house sounds pretentious unless it was used by someone highly educated or used as a joke.

…neither…nor