Words with different meanings 

What is the difference in meaning between ‘nevertheless’ and ‘nonetheless’?  Can the two words be used interchangeably? How are these words different from the word ‘notwithstanding’? Are the words used in day-to-day conversations? 
Let us consider the sentences below: 

• Maybe I’m right, maybe I’m wrong, Maybe I’m weak, maybe I’m strong

          Maybe I’m weak, maybe I’m strong         

          But nevertheless I’m in love with you

• Nevertheless I am continually with You; You hold me by my right hand. (Psalm 73:23)
• The Jallikattu protest, which the Tamil Nadu government had declared illegal, was nonetheless attended by thousands of students. 
• He was very upset and sad, but nonetheless, he controlled his emotions and played for the team.

The two words ‘nevertheless’ and ‘nonetheless’ are used as sentence connectors. We can guess the meaning of the words from the examples above. Both the words convey the same meaning.  They are similar in meaning to ‘in spite of’, ‘however’, ‘yet’, ‘anyway’ and ‘regardless’.  In many cases, the words can be replaced by ‘however’. Though the words are hardly used in day-to-day communication, the words are used mainly in formal writing.  According to Google statistics, ‘nonetheless’ is less frequently used than ‘nevertheless’. 
Though the words ‘nevertheless’ and ‘however’ are used to express a contrast, in certain cases, the words cannot be used interchangeably.  The difference is one of formality. ‘Nevertheless’ is more formal and emphatic than ‘however’.  The less formal equivalents of ‘however’ and ‘nevertheless’ are ‘in spite of this’, ‘yet’, ‘even so’ and ‘still’. 
 These less formal terms are used in spoken English.  

• I am quite busy now.  Yet, I’ll help you solve the problem.
• John is not rich and does not have a regular income.  Even so/In spite of this he helps the poor. 

The word ‘notwithstanding’ is similar in meaning to ‘nonetheless’ and ‘nevertheless’. As a preposition, ‘notwithstanding’ means ‘in spite of’ or ‘despite’ and as a conjunction it means ‘although’.  
The word is synonymous with the following:   nevertheless, nonetheless, even so, all the same, in spite of this/that, in spite of the fact that, despite this/that, despite the fact that, even though, though, after everything, however, still, yet, anyway, in any event, at any rate, at all events.  
Look at these examples:

• Notwithstanding (In spite of) his busy schedule, Robert agreed to preside over the function.
• India is considered a poor country, notwithstanding (despite the fact) that it has so many billionaires.       
• Hot weather notwithstanding, they played cricket.

Though the three words ‘nevertheless’, ‘nonetheless’ and ‘notwithstanding’ are similar in meaning, their difference is one of formality. Rarely are the words used in speaking. 

“Though the sex to which I belong is considered weak you will nevertheless find me a rock that bends to no wind.” 

– Elizabeth I