This is an unavoidable question that agents and employers will ask you every time you go for an interview.
Your strengths are what sets you apart from other testers, something that is particular to you and gives you a competitive advantage.
Here are two examples:
1. Some of the projects that I’ve worked on have been very difficult, but I have faced the challenges with determination and resilience. (be prepared to answer questions about these challenges; and not everybody is determined and resilient in face of challenges.)
2. I am very fast in writing and executing the Test Cases and so my managers have been very happy with me. (not everybody is fast when writing and executing Test Cases; the fact that you are fast may not be good if the quality of your work is not high, so if you say that make sure you also give details about your work.)
The trick with the weaknesses is to think about something that can be perceived negatively, but turn it around and make it positive.
I am very detail-oriented and sometimes I spend a lot of time on requirements – but I know that spending time on understanding requirements properly will help me write good Test Cases.
If you stop after saying “…spend a lot of time on requirements..” people will think “Oh, this is a person who never gets requirements right!”
The key is to give an explanation why you spend so much time on requirements – writing good Test Cases is a very good reason why one would spend extra time on reading and understanding requirements.
Now, grab a pen and write down a few of your strengths and weaknesses, I bet it won’t be easy. But try it anyway, it’s a very useful exercise.