Student or Learner
I feel that I can use each of these words interchangeably: "So", "Therefore", "Thus", and "Hence". I would like to know whether there is any slight difference of using any of these words if I am writing a formal text.
Here are some examples:
1- I am working hard in this shop. So, I am really tired.
2- I am working hard in this shop. Thus, I feel extremely sick.
3- I am working hard in this shop. Therefore, I urgently need some rest time.
4- I am working hard in this shop. Hence, I should get one day of absence.
As a native speaker (although not a teacher), I would break it down as follows:
1. This option is the most informal, and what you would use in conversation. "I worked very hard, so I am really tired."
2. This is a little more complex from my perspective. Here you are using 'thus' to mean 'as a result of'. It can be seen as somewhat archaic (old fashioned), and it would be uncommon in casual conversation. It would be more commonly used to indicate that is happened in the past, but can be used in the way you are describing. "Yesterday I worked really hard, thus (as a result of working so hard) I was tired." But again, unusual in casual conversation, where you would usually use 1.
3. Therefore is again possible to use in that context, but is more commonly seen in logical reasoning. "A is B. B is C. Therefore, A is C."
4. Hence is similar to 2, and can be used, but is usually in the context of future events rather than past events.
In all your examples, there are no rules against using whichever, but common usage would recommend using the simpler 'so' and being specific with your tenses.
Again, not a teacher, just a speaker. I may be contradicted by those more knowledgeable.