Example:
On Tuesday night, I went to the see doctor.
On Wednesday night, I visited my uncle's farm.
Thursday night, I stayed at home.
I saw some people using this structure on Google Books. However, I'm still not sure if it's grammatical/idiomatic to omit the "on."
In the language rules of English, "night" is a noun.
"Thursday night" is still a noun.
Nouns can't explain the actions of verbs, but adverbs can.
What you need to make it an adverb is to add the preposition "on".
I stayed at home. When? On Thursday night.
You can't normally answer that question with just "Thursday night".
So I'd assume it to be grammatically incorrect.
