Question 1: What are the nuances between using odd, weird, or strange here?
Question2: Is my example correct?
A: Did you win the lottery
B: I won the jackpot. My family does not believe I won. I have not told my other friends about this. You are my first friend to know about this.
A: That sounds odd/weird/strange. Maybe it is hiding something.
By the way, "That" refers to the whole thing B is saying.