The correct answer is C. overweening.
Overweening means excessively proud or self-confident. It is a negative term that suggests that someone is arrogant and thinks they are better than everyone else. In the context of the sentence, it is clear that the man knew everything better than anybody else, and he thought that anyone who disagreed with him was wrong. This is an example of overweening vanity.
The other options are incorrect because they do not accurately describe the man’s vanity. Overwrought means excessively emotional or agitated, overwhelming means too much to deal with, and overstrung means tense or nervous. None of these words suggest that the man was proud or self-confident.