Hyperbole, or exageration, as he is angry and trying to depict an image of the nature of man which is basically evil, and worthy of punishment and pain. He also uses hyperbole to actively describe the cause and effect of the ruin of man.
He uses social engineering, or the gathering of fake data to comply with what people need to hear and convince them to do what he wants them to do. I am not saying what he was saying was totally fake, that is up to his belief system, but certainly the manner in which he is decidedly willing to feed them this information about who we are, and what they are doing, and about how bad it is to deviate from his ways, is deceptive to a point, and geared to proving his point right.
Without knowing it, he is using the classical Monroe Motivated Sequence of persuasion which consists on:
Grabbing the Attention- If he hadn't he wouldn't have had an audience.
Trigger the need of the listener (the fact that, according to Edwards their ways will send them to hell)
Proposing a way for them to not go and burn due their actions (by changing their ways)
Visualization of an objective (in this case, he let them visualize themselves as the title states "in the hands of an Angry God" and about to be dumped in the burning flames of Hades.
Action: When he is done telling them all that they will suffer, he subtlely suggests a change of hearts and behaviors, so that they sinners can be saved.
I do not know if we can answer this question in the way you want because we do not know what specific techniques you are supposed to be talking about.
The most obvious thing that Edwards does in this sermon is attempt to frighten the listeners and thus persuade them to mend their ways. He tells them all kinds of stuff about how angry God is at them and how they deserve to go to hell.
A second thing Edwards does is to reason logically based on scripture. He does this right at the beginning of the sermon to tell them why it is likely that they will fall into sin.
Finally, Edwards offers hope. This is mainly at the end of the sermon where he tells the listeners that God has been merciful -- has "thrown the door of mercy wide open."
I hope this is useful. If not, you may want to let us know what kinds of techniques you are supposed to be looking for.