In most cases the meaning is the same.  The differences are subtle.

You need (or have to) to take the medicine.  (if you don't take it, you  may die)

You must take the medicine        (you have to take the medicine, whether you need it or not.  It is required)

You should/ought take the medicine     (it is better if you take it)

You will take the medicine                  (it is an order that you take the medicine)

You shall take the medicine                (it can be an order but less than "will"; however in a regulation, or law, it ,means "must")

Hope this answer your question.

study

I wonder if it's correct use of: "must, should, have to", in the sentences below:

You mustn't take medicine.
You should study more.
You should stop smoking.
We have to stay here.
You have obey me.
She should improve this aspect.
We must be fair.

study

I wonder if it's correct use of: "must, should, have to", in the sentences below:

You mustn't take the medicine.
You should study more.
You should stop smoking.
We have to stay here.
You have to obey me.
She should improve this aspect.
We must be fair.

Que bom!! =)