Bismillah al-Rahman al-Rahim
“According to a hadith qudsi, ‘My heavens and My earth encompass Me not, but the heart of My faithful and true servant encompasses Me.’ The servant whose heart encompasses God has become the perfect man by actualizing the Divine Form (the spiritual form) upon which he was created; having comprehended all the Divine Names, he contains within himself the form of every creature.... As the form of all the Names - all the ontological possibilities - the human substance is able to achieve a total correspondence with the entire cosmos....” 
Universes of knowledge exist within each person. The doors to these worlds are opened to only a few. Jesus (a.s.) was one who was taught by God - God Himself unfolded Jesus' potential.
“(And remember) when the angels said: ‘Mary! Lo! God gives thee glad tidings of a word from Him, whose name is Messiah, Jesus, son of Mary, illustrious in the world and the Hereafter, and one of those brought near (unto God)....’ And He (God) will teach him the Scripture and wisdom, and the Taurat (Torah) and the Injeel (Gospel). And will make him a messenger unto the children of Israel....” (Qur'an 3: 45 -49)
“In the beginning was the Word: the Word was with God, and the Word (the Divine creative intellect) was (an aspect of) God... not one thing had its being but through Him.... The Word was made flesh, he lived among us, and we saw his glory....” (Prologue to Book of John - additions in brackets are mine)
The Word might here be construed as God's creative intellect, his creative power out of which all things come into existence. The Muslim philosopher and mystic Ibn Arabi in his book “The Wisdom of the Prophets” describes the unique characteristics and divinely bestowed gifts of seven of the great Prophets. Jesus' (a.s.) defining characteristic is his creative power, manifest in his own unique creation and in his miracles. This creative power, the power of the creative word, is the same creative power through which God brought all things into existence. However this in no way implies or leads one to the conclusion of Christ's divinity. Jesus (a.s.) use of the power of God's creative word does not make him God incarnate. Having power conferred on him does not make him identical to the One who does the conferring.
Nor does the fact that Jesus (a.s.) was God's Word projected into Mary make him God - no more than Adam (a.s.) who (according to theology) was created through God's creative word without the intermediary of a human parent. If Adam (a.s.) who was thus created was not considered identical to God, why would Jesus (a.s.) be so considered.
Jesus (a.s.) was a servant of God in the sense of the hadith in which God says, “Heaven and earth cannot contain Me, but the heart of my true servant encompasses Me” or as indicated in the invocation of Shaban which describes the spiritual state granted to those whose intellects and hearts are purified and directed towards God.
“O God, grant me total separation from other-than-You and attachment to You, and brighten the vision of our hearts with the light of looking upon You, so that they may pierce the veils of light and attain the fountainhead of magnificence, and our spirits may be suspended from the splendor of Your sanctity.”(Supplication of Sha'ban)
Jesus' words in the Gospels are problematic only when seen from the viewpoint of a pre-determined and fixed theology or ideology. There is a vast and rich religious/mystical/devotional literature in both Christianity and Islam that opens up other ways, alternate avenues of seeing and understanding the figure of Jesus. This literature does not contradict the words of Jesus (a.s.) in the Gospels or the portrayal of him in the Qur'an but, in fact, adds profound depth and substance to his representation.
So what about a seemingly unequivocal statement of Jesus such as “I and the Father are one” which seems to indicate a single identity for God and Jesus. What could be a more clear indication of Jesus' divinity?
It's a fair question because it is a feature of every religion, every set of doctrinal beliefs, and even every ideology or political system, that the followers of that system believe it to be true and correct - why else would they adhere to the belief. So it is fair to inquire into how Islam might attempt to interpret such claims of mainstream Christianity - and, depending on the tone of the discussion, this can have a beneficial effect. In the case of belief systems, although we will find doctrinal disagreement, we may find that as we move to higher and deeper levels of scriptural interpretation, that the apparent differences may begin to dwindle. And even if they do not entirely disappear, we can at least achieve levels of understanding between faiths that denote true respect and understanding. And that's always a worthy goal.
So how might a Muslim approach Jesus' statement “I and the Father are one”?
The Qur'an states that Adam was created with the two (metaphorical) hands of God's power. Traditionally it is said that one hand represents the attributes (or names) of God that draw humankind near to God (e.g., mercy, love, compassion etc.). The other hand represents the attributes of distance (e.g., Majesty, Incomparability, Dominion, Kingship, etc.), those qualities representative of God's kingly attributes which accent humankind's distance from God and God's power and incomparability.
Jesus is sometimes said (because of his unique creation) to be representative of the hand (or aspect) of God that denotes the nearness of God to his creation. Whereas a Prophet like Moses who brings a law and enters into conflict with Pharaoh, necessarily primarily manifests God's Kingly and awe-inspiring qualities (alongside his other qualities). But the essence of Jesus' message powerfully focuses on God's merciful proximity to humankind and the human proximity to God. Being a sign of this dual proximity, Jesus exhibits an archetype of this type of servant-hood - the individual will is identical with that which God wills - the individual has a proximity to God, and God manifests within the individual - “I and the Father are one.” (John 10:30)
It is perhaps like the hadith which states that in respect of His true servants, He (God) is the sight with which they see, the hearing with which they hear, the foot with which they walk, and the hand with which they grasp. Such people give their being wholeheartedly over to God who takes them comprehensively into His charge - so they dwell in the Knowledge and Grace of God and He dwells in them. “I am in the Father, and the Father is in me...I speak not of myself, but the Father does the works.” (John 14:11) However, the servant remains a servant as Jesus repeatedly clarifies, carefully setting his mystical statements in context.
“Whoever believes in me believes not in me but in the One who sent me and whoever sees me sees the One who sent me.... For what I have spoken does not come from myself; no, what I had to say, what I had to speak, was commanded by the One who sent me....” (John 12: 44 - 49)
It might be said that, putting aside Jesus' divinity, he is nevertheless (according to Christians) the only way to approach God. This is clearly stated by him when he states in no uncertain terms, “No one approaches the Father but through me.” (John 14:6)
For Muslims, the Qur'an acts as quality control over what has come down to us of previous books, adjusting and compensating for what time and doctrinal interpretation may have obscured. We look through the lens of the Qur'an just as Christians and Jews look at other religions and each other through the lens of their own scriptures. This is a given. But this does not mean that we cannot respect and highlight the similarities, discuss the differences, and dialogue in good faith with one another - “and discuss with them in the most beautiful manner.” (Qur'an 16:125) We can then perhaps explore the possibility of deeper more inclusive interpretations, rather than only accepting surface-level sectarian readings. And we can see this principle was followed by some of the brightest lights of Christianity in the past, many of whom did not adopt an exclusivist stance:
As St. Thomas Aquinas said, quoting St. Ambrose, “all profound truth, no matter where it is found, has the Holy Spirit for its author.”
Again, St Justin stated: “God is the Word of whom the whole human race are partakers....” and (Meister) Eckhart spoke of an ancient sage in the following terms: “Our most ancient philosophers found the truth long, long before...ever there was a Christian faith at all as it is now.”
Thomas of Villenova taught.... “Our religion is from the beginning of the world....if you saw Abraham, and Moses, and David alongside Peter and Andrew and Augustine and Jerome, you would observe, in all essential things, a perfect identity.”
There's a profound principle in these words of great Christians, one that can allow a level of proximity (instead of exclusivity) between different faiths even if they hold doctrinal differences. When Jesus says “No one approaches the Father but through me”, he refers to those whose hearts are on his path, whose beings have a resonant identity with his, whose spirits are congruent with his - they are the ones who approach God through Jesus, even if they have never seen or heard Jesus. They cultivate an essential identity which connects and accords with the spirit and truth of his teachings though they may know little or nothing about Jesus himself. It is a person's inner reality (and the actions which spring from it) that is the deciding factor. Those whose tongues speak doctrinal words but whose inner reality is far from Jesus' are a different case:
“Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.... And every one that heareth these sayings, and doeth them not, shall be likened unto a foolish man, which built his house upon the sand.” (Matthew 7:22-27)
Jesus “took two handfuls of earth and said, ‘Which of these is the best? People are created from earth, so the most honorable among them is the most virtuous and God-conscious.’ ” (Mqjmu'ah al-Akhbar fi Nafa'is al-Athar, 106)