How strong is the need to belong? Are there any studies that measure the need to belong? 

Does this need vary greatly from person to person or is there a tight deviation?

What would explain why some have very little need to belong vs. those with a very strong need.

Also, to what extent will an individual forgo other needs to fulfill this need?
In partial answer to your question, yes, there have been several studies involved in this particular field.

Some findings include:

According to the article "The need to belong: Desire for interpersonal attachments as a fundamental human motivation" (Baumeister and Leary, 1995), concluded that


  that human beings are
  fundamentally and pervasively motivated by a need to belong,
  that is, by a strong desire to form and maintain enduring interpersonal
  attachments. People seek frequent, affectively positive
  interactions within the context of long-term, caring relationships.


An important finding in that paper is that their research found that humans more readily make social bonds and resist dissolving them.  Essentially, we tend to 'stick around' rather than walk away.  Specifically (from the article:


  Not only do relationships emerge quite naturally,
  but people invest a great deal of time and effort in fostering
  supportive relationships with others. External threat seems
  to increase the tendency to form strong bonds.


Further, according to "Psychological need-satisfaction and subjective
well-being within social groups" (Sheldon and Bettencourt, 2000), concluded with a key point related to your final question (bolding mine):


  that formal group membership may come
  with some trade-offs: one gains a more distinctive group identity, but may sacrifice
  some personal freedom. Conversely, it seems that members of informal groups are able
  to feel greater autonomy and individual uniqueness within such groups, but they may
  not derive as much pride or sense of identity from comparing their group to other
  groups (Brewer &amp;Pickett, 1999).


I hope this helps a bit.