The correct form of your first sentence is:
There are no other words for it.
We use "other" before plural countable nouns and all uncountable nouns.
We use "another" before singular countable nouns.
In your second sentence, "no" and "another" are mutually exclusive determiners and we can't use both of them in front of the same noun.
Your third sentence is also fine. Yes, when you use "other" in a non-negative and non-pre-quantified structure, you should use a plural noun after "other" (so it's not correct to say "there is other word"), but there is nothing wrong with "one other word" or "no other word".