A number of ideas connect these two plays. From similar protagonists and supporting characters to actual events in each play, the works of Miller and Sophocles offer a rich set of comparative elements. The most significant similarities are found in the protagonists.
The protagonists are characterized by a fundamental distance from factual reality. Willy Loman is delusional and incoherent. He hallucinates. Importantly, he is also dedicated to a certain illusory vision of success and achievement that has buffered his relationship to reality for quite some time.
Many critics have asserted that Willy is a modern tragic hero, and that his tragedy lies in his belief in an illusory American Dream.
Oedipus, a quintessential tragic hero, is also buffered from reality. He believes in a set of facts that are proven false as the truth of his situation is revealed over the course of the play. This false relationship to reality presents a significant similarity between the characters of Willy Loman and Oedipus.
Taking this point a bit further, we also see both Willy Loman and Oedipus actively struggling against what they perceive to be their fate. Oedipus energetically rejects the prophecy that has inevitably shaped his life.
...Oedipus struggles against the oracle that predicts his hand in his father's death and boldly asserts that it is wrong...
Willy Loman sees himself dying as a failure. To avoid such a fate, he commits suicide.
Self-inflicted harm occurs at the climax of each play. Oedipus blinds himself and Willy commits suicide. Both acts of violence are undertaken as a means to assuage and recompense wrong-doing and guilt over a failure to do "the right thing".
Female characters in both plays act as a voice of reason and restraint, advising the protagonist to take stock of the value of his life. Linda and Jocasta each attempt to persuade their husbands to abandon their quests, anticipating the tragic outcome of any continued pursuit.