This is Claudius's only significant soliloquy in the play and in it he reveals his guilt over what he has done. For the first time we hear from him how he feels about his actions. He clearly recognizes that he has committed a terrible sin and he would like to be forgiven that sin, but in the end he knows that if he doesn't give up the gains from that sin (the throne and Gertrude) then he will never be forgiven by God.
Here are two quotes that have several of the literary devices you are asked to consider:
What if this cursed hand / where thicker than itself with brother's blood, is there not rain enough in the sweet heavens to wash it white as snow?
In this quote there are a couple of things to notice. The image of the thick blood of his brother is very powerful. The "thick" makes it heavy and vital and the fact that it is thicker than his hand suggests an overwhelming amount of blood. Blood is usually a symbol of life. In this case it is spilled blood, and therefore symbolic of a loss of life -- King Hamlet's. It is also an allusion to Cain's murder of his brother Abel from the Bible. This is traditionally considered the first murder -- these are the children of Adam and Eve.
Rain is usually symbolic of cleansing -- both physical and spiritual. Here it is a symbol of heavenly cleansing, or God's forgiveness. He is thinking that there is not enough forgiveness from God to cleanse him of his sin.
He later uses hand imagery again. He says,
In the corrupted currents of this world / Offense's guilded hand may shove by justice / And oft tis' seen the wicked prize itself / Buys out the law.
Here, Claudius is calling his hand gilded which means it is covered over with a thin layer of gold (but what is under the surface is considerably less worthy or valuable.) What he really means that he is now has all the power of the kingdom because he is king (the "wicked prize", and as king, he will likely get away with his crimes because no one will dare to suspect him and charge him with the crime. In this case, no one knows that a crime even took place, but perhaps that is because no one dared to investigate the story. His gold hand was able to shove justice away from his guilty acts. The strong imagery and symbolism again come into play in order to illuminate Claudius's guilt.