This is a good question. There are several ways in which Oedipus destroys the lives of others. Let me give you a few of these ways.
First, on the most general level, he brings suffering to the people of Thebes. In the beginning of the story, there is a huge plague in Thebes on account of the transgression of Oedipus (he killed his father and married his mother).
Second, Oedipus also ruins the life of his mother, as he marries her. When Jocasta finds this out, she commits suicide, as she cannot take the truth.
Third, he also ruins the lives of his children as he becomes a plague to all people. As we follow the Theban trilogy, we see that his sons kill each other and Antigone also dies a miserable death as she seeks to bury her deceased brother. In a word, Oedipus' famliy is seriously dysfunctional.
In conclusion, Oedipus brings grief to many. However, the important point to keep in mind is that he is a tragic hero, that is, he unwittingly brings destruction. Here is one of the most famous quotes:
People of Thebes, my countrymen, look on Oedipus. He solved the famous riddle with his brilliance, he rose to power, a man beyond all power. Who could behold his greatness without envy? Now what a black sea of terror has overwhelmed him. Now as we keep our watch and wait the final day, count no man happy till he dies, free of pain at last.