The greatest difference between the portraits of Jesus according to Matthew, Luke, Mark and John is that whereas Matthew, Luke and Mark paint portraits of Jesus as a natural man who has elements of divinity, John paints a portrait of Jesus as divine and the earthly extension of God.

For instance, Matthew Chapter 1 presents the most extensive tracing of Jesus's genealogy in order to establish his earthly authority, whereas John Chapter 1 presents the divine "genealogy" of Jesus by identifying him as the "Word" and associating him with an active part in the Creation in order to establish his divine spiritual authority:

[The] Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. ... The Word became flesh and made his dwelling among us ....  (John 1:1-3 & 14 New International Version)

In contrast, Luke Chapter 1 begins "to draw up an account of the things" (NIV) that happened in Jesus's life and emphasises his affinity with humankind by giving details of such things as Mary's experience and relationship with her cousin Elizabeth. Whereas Luke takes a corporeal focus, John continues to take a spiritual focus by using incidents to pronounce Jesus's spiritual identity, as when John narrates how Jesus feeds the multitude, then identifies himself as the spiritual "Bread of Life":

Then Jesus declared, “I am the bread of life. Whoever comes to me will never go hungry, and whoever believes in me will never be thirsty. (John 6:35)

Mark 1 starts out on yet a different tack by connecting Jesus to Old Testament prophesies of a messenger to come who will proclaim the presence of the "Lord," who is otherwise called the Messiah:

And this was [John the Baptist's]  message: “After me comes the one more powerful than I, the straps of whose sandals I am not worthy to stoop down and untie (Mark 1:7)

While John Chapter 1 addresses the same prophetic point,

John replied in the words of Isaiah the prophet, “I am the voice of one calling in the wilderness, ‘Make straight the way for the Lord.’” (John1:23)

this Gospel differs from Luke by focusing on addressing the question, "“What sign can you show us to prove your authority to do all this?” (John 2 18), while Mark focuses on describing the miracles of physical healing Jesus performed:

That evening after sunset the people brought to Jesus all the sick and demon-possessed. 33 The whole town gathered at the door, 34 and Jesus healed many .... (Mark 1:22)

In the four Gospels found in the New Testament of the Bible, John provides a description of Jesus' ministry before he was crucified. The author of the book of John (and there is controversy over who actually wrote it) concentrates on Jesus as the incarnation (physical manifestation) of God, or rather, "God incarnate."

John presents Christ as Christ presented himself:

Jesus answered, “I am the way and the truth and the life. No one comes to the Father except through me." (John 14:6 NIV)

John describes Jesus—the man and his works are so much more meaningful than they may first appear. John explains that Jesus is he who will guide believers onto the path to everlasting life; from there he will guide his followers to Heaven, the place from which he descended in the form of a man.

Matthew, Mark and Luke are synoptic gospels, meaning they share the same stories and sometimes even the same wording.

Based on research, Matthew, by inference, portrays Jesus as a man who is intellectually and spiritually grounded, yet loving and caring as well. If Matthew did indeed write this book (and scholars disagree), he was a man dedicated to Jesus while he was alive, and then spoke publicly, proclaiming Jesus as the Messiah after Christ was crucified and resurrected.

In the book of Mark, the author portrays Christ in a much stronger, and certainly more powerful manner than the other gospels:

Its swift narrative portrays Jesus as a heroic man of action, an exorcist, a healer and miracle worker.

Scholars observe that Mark portrays Jesus as a man who did not act like a messiah during his lifetime. During his life, Jesus did not encourage the disciples to identify who he was. The purpose for this has also resulted in a good deal of debate.

The final books is Luke's, the longest of the four gospels. Once again, there is disagreement as to who actually authored Luke.

The author portrays Christianity as divine, respectable, law-abiding, and international...

…and Christ is portrayed as one who exercises compassion for all, including those who were needy (the poor) and women (who were traditionally "second-class citizens in Jewish society and worship). In Jesus' tale of the "Good Samaritan," the Samaritan—of a race that was generally despised by the Jews—is praised for his compassion of the Jewish man who is robbed, left to die and ignored by the Levite and even a priest who pass by. In Luke we see Jesus as a figure with arms wide open in acceptance: even Gentiles were given the opportunity to learn of the Word and find salvation.

Additional Sources:

http://www.enotes.com/topic/Gospel_of_Luke

http://www.enotes.com/topic/Parable_of_the_Good_Samaritan

http://www.biblegateway.com/passage/?search=John+14%3A6&version=NIV

http://www.infidels.org/library/modern/james_still/gospel_john.html

How does each gospel characterize Jesus differently?Give the portraits of Jesus according to Matthew, Mark, Luke and John.

The writers of each gospel, though telling the story of the same man, Jesus Christ, each  present him in a very different and very personal way.  Literary elements which affect the characterization of Jesus include what events, stories, parables, and miracles they choose to tell and what is left out, the different names they use for Jesus, as well as the order in which each gospel is presented.

As such, the Gospel of Matthew portrays Jesus' kingship, or Jesus as King.  This is evidenced by referring to him as the Son of David as well as the major thematic focus of the gospel on the kingdom of heaven.

The Gospel of Mark focuses on the humanity of Jesus, who is portrayed in this book both as the "Son of God" and the "Son of Man."  More than 40% of the Gospel of Mark focuses on the suffering and sacrifice of Christ's final week on earth.

The Gospel of Luke portrays Jesus as a teacher.  Luke provides the greatest variety of teachings, parables, and events from the three year ministry of Jesus.  Additionally, Luke provides the most evidence of Jesus' interest in Gentiles (non-Jews) and the poor.

The Gospel of John, written by the disciple whom "Jesus loved," portrays Jesus' "sonship" or, connection to God the Father.  John refers to Jesus as the "Son of God," the "Lamb of God," the "Messiah," and the "Savior of the world."  John outlines seven miracles of Jesus which end in his resurrection, all of which are proof that he is the Son of God.  Finally, John includes several sermons of Jesus not found in the other gospels which help explain the purpose of his life.