"They do not teach us this word in school!"
Translation:Ve škole nás tohle slovo neučí!
There are many acceptable word orders, but this is not one of them. It is hard to say why though. "Nás tohle slovo ve škole neučí!" is fine. "Tohle slovo nás ve škole neučí!" also fine.
I am confused as to what you mean by the subject of this sentence. In English, the subject is "they". In English "us" is the indirect object. Is "nas" considered the subject in the Czech sentence?
Indeed, the mention of a subject was a mistake on my part. I am not sure about the ultimate explanation anyway. The proposed word order is unnatural and "nás" should likely come earlier.
So nás should be earlier than neučí? Is that the reason why neučí nás tohle slovo ve škole is wrong?
Neučí nás tohle slovo škole. is a grammatically correct sentence, but not very natural. You are stressing AT SCHOOL so I would assume you are telling that they don't teach you the word at school but somewhere else.
But perhaps it can be added anyway.