MAXDOP or 1 only? Or sql can use a value between 1 and configured maxdop Is there a way for sql server to use no of cores which is between 1 and the configured MAXDOP? 

For example if maxdop is 8. Is it possible for sql to use 3? Lets say that resource gov, hints, and any other control mechanisms are not in place. 

Or is it simple 1 for singlethreaded and 8 for parellelized?
When you set MAXDOP = 8 this is not saying that the Degree of Parallelism will be 8 cores for your process.  It means that no more than 8 cores will be used for your process.  

It could use only 1 core up to 8 cores with that setting.  This all depends on many other usage factors such as when several long processes are running on your server.  The SQL Server tries to manage the processes so that every running process gets some CPU time allocated to it very regularly.

https://www.brentozar.com/archive/2014/11/many-cpus-parallel-query-using-sql-server/

Brent's post also verifies that Paul White has audited Kendra Little's post as correct. (Just in case you want more verification.)

Again from Paul White from a discussion at http://www.sqlservercentral.com:


  The instance-wide MAXDOP setting sets the maximum possible degree of
  parallelism. A setting of zero (the default) allows SQL Server to use
  as many threads as there are processor cores that it is configured to
  use.
  
  The cost threshold for parallelism is only used by the optimizer. 
  If the cost threshold is set to 5, the query must have an estimated cost of
  at least 5 before the optimizer will look for a parallel plan
  alternative.


In a case like that a MAXDOP 8 setting for the query may not exceed the cost threshold and thus will not create a parallel plan.

If you have a process where you specifically need to manage resources, more than 1 but less than the MAXDOP setting, you could add the OPTION (MAXDOP 4) (as an example) or some other setting that would fit the process you are running.

Therefore, you have some choices and are not stuck with just: 1 core, 8 cores, or "all" processors.