Describe the importance of omens and the supernatural in Julius Caesar?
As explained in eNotes' "Introduction" in the Study Guide:
Probably written in 1599, Julius Caesar was the earliest of Shakespeare's three Roman history plays. Like Antony and Cleopatra and Coriolanus, Julius Caesar is a dramatization of actual events, Shakespeare drawing upon the ancient Roman historian Plutarch's Lives of Caesar. Brutus, and Mark Antony as the primary source of the play's plot and characters.
Plutarch attaches great importance to omens and the supernatural. According to Salem's Encyclopedia of the Ancient World:
His most famous work, the Bioi paralleloi (c. 105-115 c.e.; Parallel Lives, 1579), is organized into pairs of biographies of statesmen and military leaders, each pair consisting of the life of a Greek and that of his Roman counterpart (for example, Alexander the Great and Julius Caesar).
Plutarch's writings are full of references to the Greek and Roman gods and to omens, prophecies, and supernatural phenomena.
Shakespeare, however, could not have shared Plutarch's beliefs. He used ghosts, omens, and other supernatural material for different purposes in his play Julius Caesar. For one thing, they evoke the feeling of the time when everyone, including Julius Caesar himself, shared such superstitions. They help to carry the audience back into the remote past. They seem to be witnessing great historical events involving such famous men as Caesar, Antony and Brutus.
Shakespeare also used the supernatural to solve his biggest plot problem. Julius Caesar dies in the third act. Many critics have suggested that Brutus is actually a much more important character and ask why the play should not be named after him. Shakespeare used Plutarch to suggest that Caesar's body may have been killed but his powerful spirit continued to direct events until the very end of the play, and thus he was justified in naming it after Julius Caesar.
However, the great guardian-genius of the man, whose help he had enjoyed through life, followed upon him even after death as an avenger of his murder, driving and tracking down his slayers over land and sea until not one of them was left, but even those who in any way soever either put hand to the deed or took part in the plot were punished.
Shakespeare relied heavily on this passage. Caesar did seem to have had a great guardian-genius "whose help he had enjoyed through life." He seemed invulnerable and invincible. Whatever he was determined to accomplish, he did accomplish despite adversities and appalling odds. His soldiers idolized him. They would follow him anywhere. His enemies must have been terrified of him, since it took so many of them to assassinate him.
Shakespeare also used Plutarch's frequent descriptions of supernatural phenomena to foreshadow the assassination which takes place in Act 3, Scene 1. Because of all the foreshadowing in the first two acts, as well as the additional foreshadowing in the first part of Act 3, Scene 1--including the following, borrowed directly from Plutarch:
[To the Soothsayer] The ides of March are come.
Ay, Caesar; but not gone.
--the audience is led to believe that Caesar's death will be the climax of the play and might indeed be the conclusion.
Shakespeare, however, wanted to make the assassination anticlimactic and actually disappointing to his audience, because he intended to use Marc Antony's great funeral oration as the most dramatic moment and the pivotal point in the play.