The Great Awakening was characterized by colorful sermons that appealed to the emotions of the listener. Explain how this characteristic can be seen in Edwards' sermon "Sinners in the Hands of an Angry God"?

Edwards definitely uses pathos or an appeal to the emotions in his sermon. This characteristic rhetorical device is utilized to provoke strong emotions like fear, anger, and/ or despair in an audience. Experienced orators or preachers appeal to the emotions of their listeners to try to inspire them to enact changes in their lives.
There are many places in Edwards' sermon where he tries to inspire fear in his audience. For example, he warns his listeners that the fires of hell are just about ready to consume them and that God is angry with more of them than they think.

Yea God is a great deal more angry with great Numbers that are now on Earth, yea doubtless with many that are now in this Congregation, that it may be are at Ease and Quiet, than he is with many of those that are now in the Flames of Hell. . . The Wrath of God burns. . . Damnation don’t slumber, the Pit is prepared, the Fire is made ready, the Furnace is now hot, ready to receive. . . the Flames do now rage and glow.

Throughout the sermon, Edwards piles on the emotional rhetoric; he means to frighten his listeners into submission and whip them into a frenzy of fear and despair. He paints the picture of the devil standing by, ready to "fall upon them and seize them as his own, at what moment God shall permit him." Without fail, he emphasizes over and over again the image of a God who harbors "unmixed, unrestrained wrath" towards those who choose not to repent.
Later, he asserts that the only way to escape such damnation is to be "born again." Soon after, he casts doubt on who has actually achieved this envied status. Edwards thunders that he has "Reason to think, that there are many in this Congregation now hearing this Discourse, that will actually be the Subjects of this very Misery to all Eternity." In fact, he maintains that any one of them listening to his sermon may well end up in the fires of hell.
Edwards keeps his audience in a state of panic and disequilibrium by veering between conflicting, vague statements. On one hand, he promises that those who repent will escape the fires of hell. He also proclaims that most people are less safe than they think. He gives his listeners the impression that, no matter what they do, they are very likely to be doomed to the fires of hell. Edwards definitely appeals to the emotions of fear and despair as he speaks to his audience.