So and then are used all the time in speaking. Thus and thereby are old fashioned words that most people no longer use.

From a book corpus, which definitely skews towards formal language: Frequency list: so = about 40th then = about 80th thus = about 300th thereby = about 3100th So is around the 40th most common word in written English. They are all common. The top 5000 words are all quite common, but the top three words given are WAY more common than thereby. Note: "So" is about 100 times more common in general than "thereby."

'So' is the most common, and means the same as 'therefore', which is formal but also common. It's used to show a reason and result of something. (I'm very tired, so I'm going to sleep). You can also use 'so' to begin a sentence or change the subject of a conversation. (So, what do you want for dinner?) 'Then' is just as common, but the meaning is a little different. Use 'then' for 'in that case', especially with 'if'. (If I feel tired, then I'll go to sleep). 'Thus' and 'thereby' are both very formal and not common. You probably won't hear or use them except in formal or academic writing.

The first two are most used in casual form. "Thus" is more formal. "Thereby" sounds very legalistic and therefore most formal in a commanding way, like reading out a statute or the terms of a contract.