How does one relate Qur'an and Sunnah with the four great Sheiks namely, Shafii, Hanafi, Maliki, and Hanbaly? Is the role of these great Sheiks to divide Islam into sects? What the does Qur'an Surah 6:159 relate to?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

One should not subject the Quran and Hadeeth to the opinions of great Imams or scholars but the opposite is correct. Those opinions which conform to the Quran and Hadeeth would be accepted and those which are not so, would be rejected. Every Imam has stressed the importance of following the sound Sunnah and advised Muslims to leave any opinion that contradicts them [Quran and Sunnah]. The sayings of every human being can be accepted or rejected except the sayings of the Prophet Muhammad (who is infallible). Thus, to believe that the role of known Imams such as Imams Abu Haneefah, Ash-Shaafi’i, Maalik, Ahmad Ibn Hanbal and others, is to split the Ummah (Muslim nation), is a great injustice to them and denies their tremendous efforts to unite the Ummah in knowledge and correct guidance.

In fact, these scholars sacrificed themselves to the cause of Allah. They devoted their lives to call people toward Islam and to teach them Islam. They tried their best to issue the correct Fatwa based on their Ijtihaad [for definition, please refer to Fatwa: 90732] regarding contemporary matters they faced at that time.

Making Ijtihaad while there is no clear evidence is permissible and only an ignorant person will deny it. Sometimes the companions of the Prophet Muhammad used to make Ijtihaad during the reign of the Prophet Muhammad and he used to correct the mistaken ones and to approve those that were correct.
Sometimes, he approved both understandings as he did in the case of the Companions, may Allaah be pleased to them, while they were going to Banu Quraydhah. Imam Al-Bukhari narrated that the Prophet said: “None of you (Muslims) should offer the 'Asr prayer but at Banu Quraydhah’s.”. The 'Asr prayer became due for some of them on the way. Some of them said, “We will not offer it till we reach the place of Banu Quraydhah.”; while some others said, “No, we will pray at this spot, for the Prophet did not mean that for us.” Later on, this was mentioned to the Prophet and he did not berate any of the two groups.”

As for the meaning of the verse you referred to in the question, it means those who divided their religion believing in a part of the religion and rejecting the other.

Muslim scholars held different opinions concerning the people meant by this verse, whether they are Jews only or Jews and Christians? The later opinion is more correct for the verse in which Allah says (what means): {And the people of the Scripture (Jews and Christians) differed not until after their came to them clear evidence. (i.e. Prophet Muhammad and whatever was revealed to him.} [Quran 98:4]

It is also said that the above verse refers to pagans since some of them worship idols, some worship angels and some worship stars and so on, thus they are divided into groups and have no common religion. It is also said that this verse refers to the deviant people of this Ummah.

The most correct opinion, however, is that this verse refers to all the non-Muslims and those who introduce innovations in the Sharee’ah. As long as the words of the verse do not identify a certain group, it is better to generalize its meaning to all non-Muslims and innovators.

Finally, the Ijtihaad of the previous Imams is a good deed and they will be rewarded for it, Allah willing. The difference in their opinions is only superficial; it does not affect the basics of the Sharee’ah and it is based on sound evidence from the Sharee’ah.

Know that this verse or the like does not mean the differences based on Ijtihaad.

Allah Knows best.