Okay I typed out a really long answer to this and then lost it, so I'm going to cut it down a little bit, and if you have any more questions feel free to ask. Here we go.

Evidence from Orderic Vitalis and the Domesday Book suggests that Norman settlement was ruthless. Initially, William I allowed many of the Anglo-Saxon lords to retain their lands, but in the years after the Conquest, frequent rebellion led to him changing this policy. Notably, the invasion of Sweyn II in support of Edgar the Aetheling, resulted in a brutal destruction of the northern provinces (known to history as the Harrying of the North) and significant redistribution of lands.

There were also a lot of problems stemming from the fact that English and Norman systems of lordship were very different. Tenurial bonds in Normandy were much stronger than they were in England, as Feudalism was taking on a much more standardized shape on the continent. In England, a man could be bound to a lord, but not hold any land from him. A lord might hold jurisdiction over land, but not actually be the landlord. Or you might have what was called a "commendation", which was a purely personal bond that had neither jurisdictional or tenurial content. When Normans took over the roles of these Anlgo-Saxon lords, they imposed a distinctly Norman system of lordship on these people, assuming the role of landlord over everything within their jurisdiction. This obviously led to a lot of disagreements and ultimately ended in the Norman lords interpreting (or intentionally misinterpreting) the rights of their predecessors to further their own interests.

This was exacerbated by shameless land-grabs throughout England. From Marc Morris's The Norman Conquest:

There is abundant evidence to show that, while much of the land was given out by the king and entered into legally, a considerable amount was acquired by less than legitimate methods -- extortion, intimidation, and violence. In certain areas of the country -- the east Midlands and East Anglia -- the Domesday Book shows no clear pattern of land-distribution, which has been interpreted as indicating the Norman settlement of these regions was something of a free-for-all. More concretely, Domesday also preserves the testimony of local jurors that certain Normans had helped themselves.

Notable among these Normans were Richard fitz Gilbert and Odo of Bayeux (half-brother of William and commissioner of the Bayeux Tapestry). Richard was granted Tonbridge, Kent, but soon seized manors in Surrey and ecclesiastical lands in Rochester. Odo, in his time as Earl of Kent, held estates scattered throughout 22 counties, many of which he obtained in a way that so disregarded law and equity that Oderic Vitalis labeled him a tyrant.

Through these ruthless policies, the Anglo-Saxon elite were all but destroyed through either demotion, exile, or displacement. Within a couple decades of the Conquest, the Anglo-Saxon elite essentially didn't exist anymore. There were still Anglo-Saxon nobles, but they would have all be under a Norman lord.

The time was marked by nothing but rebellion and conflict. Eventually things died down, but the damage had been done.

As for intermarriage and migration of non-elites, I don't really know anything about that specifically, but I hope this comment was illuminating.

/u/freeogy is right to emphasise the violent aspects of Norman England, but like in all history, the Norman Conquest wasn't entirely a disruptive event. Allow me to present the case for continuity after 1066 :)

It is true that the Norman concept of tenure was different from the Anglo-Saxons, but it was only a matter of extent, as Norman tenure wasn't exceptionally tidy either, with Norman pledges of service being often ad-hoc and containing very different terms of service. Edward the Confessor had already brought Normans into England during his reign, making men such as Ralph the Timid the earl of Hereford and Robert of Jumièges the Archbishop of Canterbury. His earls also knew a great deal about the Continental world - Harold Godwinson had experienced Normandy firsthand, whilst his brother Tostig had married into the Flemish nobility. Though Normans imposed their system post-Conquest, it was probably already familiar to the Anglo-Saxon elite, and the Normans in any case were happy to pretend they were just continuing the old system - remember William I claimed to be the legitimate successor of Edward the Confessor, so he couldn't change the institutions wholesale. We for instance have records of William being acclaimed by Anglo-Saxon nobles, rather than him brutally imposing his will (these accounts were from pro-Norman chroniclers, but they were contemporary and were surely reflective of the fact that the new regime still needed Anglo-Saxon support to function, propaganda is still a useful source for contemporary attitudes!). There is also the Anglo-Saxon Chronicle's account of his coronation: 'and he [William] promised Ealdred on Christ’s book and swore moreover (before Ealdred would place the crown on his head) that he would rule this people as the best of the kings before him, if they would be loyal'. As far as I remember, Ealdred was a moderating influence on the king until he died, so William definitely did not discard the existing nobility entirely.

At least at the beginning of his reign therefore, William was nothing if not conciliatory, and though in later years there were revolts, there are indications that he at least tried to carry on aspects of Anglo-Saxon administration. In 1086, again in the Anglo-Saxon Chronicle, William received an oath from all men of worth in England at Salisbury, indicating that he was still trying to preserve continuity - though no Anglo-Saxons held earldoms (there were a few, but they got murdered and/or revolted, so not entirely William's fault), their voice still had weight. The Chronicle is generally negative about the Normans, but I see this passage (and the above quote about the coronation) as subtle clues that the Normans were at least trying to maintain peaceful relations with their dispossessed neighbours. In this instance, we can look at how the Anglo-Saxon kings often received advice from representatives of the realm, such as when Edward the Confessor was persuaded to abandon the tax used to maintain mercenaries only a few decades earlier. Here, I would suggest that William was deliberately trying to deal with his elites the same way the Anglo-Saxons did. For some historians, such as James Campbell, Anglo-Saxon government was actually a highly-efficient bureaucratic machine and thus worth conserving. Recent historians like Steven Baxter have weakened this somewhat, but it is still generally agreed that Anglo-Saxon institutions were pretty great and that the Normans did try to preserve what they didn't have to destroy. Normandy was by all account less efficiently governed than England, so where else could the roots of the highly bureaucratic Angevin administration have come from?

We can for instance look at legal evidence. William did not throw away Anglo-Saxon legislation wholesale (which is now seen as quite sophisticated), but only changed things to suit his preferences, such as by giving ecclesiastical courts jurisdiction over violations of canon law - which I believe was in the spirit of the papal reform movement, whereas pre-Conquest England was rather out of touch on these issues. The same was true for newly imposed lords. There is a remarkable document from 1070s recording a trial at Pinnenden Heath, in which Lanfranc and Odo argued over jurisdiction. The court ordered an assembly to be gathered of 'not only all the Frenchmen in the country, but also and more especially those English who were well acquainted with the traditional laws and customs of the land'. Particular regard is given to Ægelric, bishop of Chichester, so frail that he must be brought on a cart, who was 'a man of great age and very wise in the laws of the land, brought… in order than he might expound the ancient practice of the laws'. Law was therefore respected and the Anglo-Saxon elite still trusted, even as Odo sought to expand his holdings!

More generally, historians such as Brian Golding argued that minor lordships did survive and that the mass confiscation after 1066 only looked 'big' because the Godwinsons' estates and the royal demesne formed such a large chunk of England. Other than these redistributions, land didn't change hand much unless someone revolted/died. Others, such Henrietta Leyser, noted that many women played an informal role in Norman households (female claimants to land were often married to secure land for new Norman landowners), as they influenced their new family's policies towards neighbours (such as over competing claims from the past), and more subtly, shaped their children' views to be less Norman, but more English. We can look at the example of Gunhild, Harold's daughter with Edith Swan-Neck, who became the mistress of Alan Rufus, possibly to secure his hold over Anglo-Danish holdings such as Richmond, as Edith owned a lot of land in Anglo-Danish areas.

I'm going to end with a few quotes from Pauline Stafford, who I think most persuasively argued for continuity after 1066. For her, 1066 'was neither the first conquest nor the first succession dispute of the century'. William, although judged to be harsher than previous kings, 'shared the long established oppressiveness of English royal power'. Continuity remains in English estate officials and sheriffs, and new lords inherited old disputes - their 'injustice was debatably Norman, [their] powers emphatically English'. Moreover, she saw the Domesday Book as an attempt to record Anglo-Saxon knowledge about laws and land, which was apparently dying out - it was necessary for the Normans to write down local traditions to solve new disputes! Even landholding didn't change that much, since she saw it simply as a matter of one military elite replacing another. Conflict did occur, but I think it would be a mistake to dismiss these instances of continuity simply as exceptions, but instead see Norman England as a place of contradictions, of a new elite struggling to deal with ruling an unruly country, using both coercion and co-operation in equal degrees.