今夜は徹夜で勉強するぞって英語でなんて言うの？

I will pull an all nighter to study. - We can use the phrase 'all nighter' to express that we will stay up all night. We add on 'to study' to show the reason for the all night.

I will study through the night. - When we use the term 'through the night' it implies that we will be doing something all night. In this case, studying. You can, however, place other verbs in this sentence if you want.

I will dance through the night.
I will sing through the night. (Your neighbours might not like this)

I will stay up all night studying. - This is a more simple sentence stating that you will stay up all night in order to study.

These are very common phrases used for college students.
"Pulling an all nighter" = staying up all through the night in order to study for an exam or finishing a project/paper that is due the next day.
"Up all night studying" = to study throughout the entire night instead of sleeping.

To burn the midnight oil =To work studiously, especially late into the night.
"He was burning the midnight oil to finish his paper."
This expression may not exactly mean 'all through the night' but it is a useful one meaning 'night study.'
To study through a period of time:
"I'm going to work through the winter and then holiday all summer."
"I'm going to work through my lunch hour and go home early."

The idiom 'burn the midnight oil' means to stay up all night studying, usually for an examination the following day. The noun 'daybreak' means 'dawn', the time in the morning when daylight first appears. Most students do stay up the whole night studying if they do have an examination the following day. The common belief is that if you revise your subject thoroughly the night before the exam, you have a big chance of passing it.
So, you may say:
I am going to burn the midnight oil tonight because I have an exam tomorrow.
or
I will study all night tonight.
or
I will study until daybreak tonight.