It is best to be open and honest about weaknesses, demonstrating forthrightness and a capacity for self-critique, and to be decisive and targeted about strengths to gain advantage in consideration for a given position. This two-pronged approach requires a capacity for open self-assessment.
It is common for career advisers to recommend presenting a strength as a weakness. This often takes the form of the interviewee representing themself as a perfectionist or as "too hard-working," and it is an indicator of dishonesty to the employer. It is better simply to give an honest self-assessment and for the interviewee to present an actual weakness.
When an interviewee answers questions about their greatest strengths, it is imperative that they know what the job requires. Their exceptional skills in varied disciplines may have no bearing on the skills demanded by the position they are interviewing for. They should tailor their answer, while remaining honest, to suit the demands of the position.
The two pillars of answering these questions well and accurately are honesty and foreknowledge. An interviewee should walk into a room with confidence and a full understanding of the job they intend to interview for. Displaying knowledge about what their position demands, their suitability to meet those demands, and a degree of humility and self-awareness will give them a shot at the prize.