One of Oedipus’ strengths as a King is his self-assurance. This has brought him the powerful position that he finds himself in, being universally respected and loved by his subjects.
However, as a man, this easily morphs into arrogance. This led Oedipus to searching for a resolution to his questions himself, rather than being cautious, as he is advised by numerous others to do. His brash and rushed investigations, however, leads to the fatal discovery and ultimate ruin for the king.
On the other hand, another strength Oedipus achieved as a man and a husband is his sense of responsibility. He takes full responsibility for his family, even at the end, when the extent of his mistake becomes clear. He remains loyal to his family and takes responsibility in the best way he can see available to him, by blinding himself and accepting banishment from his kingdom and all he loves.
Ultimately, Oedipus becomes a sympathetic character because his strenghts outweigh his weaknesses, with courage perhaps being his ultimate strength as a king, a husband, and a man.