I want to save the Word document in HTML using Word Viewer without having Word installed in my machine. Is there any way to accomplish this in C#?
You will need to have MS Word installed to do this, I believe.
Check out this article for details on the implementation.
According to this Stack Overflow question, it isn't possible with word viewer. You will need Word to use COM Interop to interact with Word.
I think this will depend on the version of the Word document. If you have them in docx format, I believe they are stored within the file as XML data (but it is so long since I looked at the specification I am perfectly happy to be corrected on that).
Using the document conversion tools available in OpenOffice.org is probably the only possible option - the .doc format is only designed to be opened via Microsoft products so any libraries dealing with it will need to have reverse engineered the entire format.