Allusion in Crime and Punishment
Much of the novel discusses morality and sin and has allusions to tales and characters from the Bible. Russia has historically been an Orthodox Christian society, and many of the references to sin and redemption relate to appropriate bible passages from books like Matthew, Psalms, and Revelations. Of particular note is the allusion to the story of Lazarus, a man whom Jesus raised from the dead and gave new life.
Allusion Examples in Crime and Punishment:
Part I - Chapter II
"Image of the Beast and with his mark..." See in text (Part I - Chapter II)
The "Image of the Beast" is an allusion to the Book of Revelations and refers to the sign of the antichrist in the Christian religion. Being made in this image, as opposed to in God's image, suggests that the person possesses sinful qualities and is undeserving of Heaven's reward of life after death.
"wax before the face of the Lord; even as wax melteth!..." See in text (Part I - Chapter II)
This line is an allusion to the Biblical book of Psalms 68:2. Marmeladov uses this reference to emphasize the good qualities of Ivan Afanasyvitch, who, as we shortly learn, was willing to financially assist Marmeladov--hence the praise of his character.
Part II - Chapter I
"Noah's Ark..." See in text (Part II - Chapter I)
The Biblical story of Noah's Ark involves Noah securing pairs of all the world's animals into the safety of his boat (ark) before God sends a flood to Earth. The head clerk Zametov likely uses this expression to mean that the building is very large and full of different people, making it difficult for anyone to have seen the murderer.
Part III - Chapter II
"thrice accursed yesterday...." See in text (Part III - Chapter II)
Similar to the "three fishes" statement at the end of the preceding chapter, Dostoevsky alludes to the Trinity---a religious symbol that groups God, Jesus, and the Holy Spirit together. This allusion reinforces the underlying themes of Christian redemption in the novel.
Part III - Chapter IV
"Romeo..." See in text (Part III - Chapter IV)
Raskolnikov makes an allusion to Romeo, one of the titular characters from Shakespeare's Romeo and Juliet. This makes it clear that Raskolnikov is teasing Razumihin about being in love with Dounia, since calling someone a "Romeo" implies that they are lovestruck.
Part III - Chapter V
"Lazarus’ rising from the dead..." See in text (Part III - Chapter V)
Porfiry refers to the biblical story of how Jesus raised Lazarus from death. Considering the themes of redemption and rebirth in the novel as they pertain to guilt, this question is less about Porfiry's curiosity and more about Raskolnikov's belief in the possibility of redemption.
Part VI - Chapter II
"Seek and ye shall find...." See in text (Part VI - Chapter II)
Porfiry alludes to a passage from biblical book of Matthew 7:7-8 (also found in Luke 11:9-10) to make his point that Raskolnikov ought to realize that life has meaning and is worth living. The biblical verse not only reinforces the theme of redemption in the story, but it also helps to provide context for Raskolnikov to understand that he does not have to be destined for punishment if he only seeks out forgiveness.
Part VI - Chapter VIII
"If I must drink the cup what difference does it make?..." See in text (Part VI - Chapter VIII)
Raskolnikov alludes to Jesus's comment in the Garden of Gethsemane, where Jesus asked God to take a symbolic cup, or burden, away from him. By saying that he must drink the cup, Raskolnikov indicates that he is ready to accept the suffering he must face for the crime he committed.
Epilogue - Chapter II
"the age of Abraham..." See in text (Epilogue - Chapter II)
The story of Abraham features prominently in Judaism, Christianity, Islam, and all Abrahamic religions. The choice of "age of Abraham...had not passed" in this passage in meant to invoke a feeling of the ancient and ideal past before the troubles and worries of modern civilization.