Function for getting strings consisting of random characters
My immediate thought is that the function is just doing too many things. 

It'd be simpler to just return a mixed-case string of a specific length. Done.

Want that string to be all-uppercase? Just call getRandomString(n).toUpperCase().
All-lowercase. Call getRandomString(n).toUpperCase().

Want it to have a separator between each letter? Call getRandomString(n).split('').join(separator).

Want it be be somewhere between x and y characters long? Pick a random length yourself, and pass that to the function.

This just seems like a function built for a very narrow purpose. For instance, what if (for whatever reason) you only want a separator every 4 characters? Do you add yet another argument to the function, or do you write a separate function to chopping and glueing the way you want it?

Even if you need a single function to do everything, it'd be simpler to have it just call out to other functions that comprise the building blocks. Lots of the functions you need already exist (toUpperCase, toLowerCase, split, and join), so it's only the randomness you need to add.

A simple and crude structure might be:

function getRandomInt(min, max) {
  var span = parseInt(max, 10) - parseInt(min, 10);
  if(span &lt;= 0) {
    throw { message: 'Min must be less than max.' };
  }
  return min + Math.round(Math.random() * span);
}

function getRandomLetter() {
  var asc = getRandomInt(65, 116);
  if(asc &gt; 90) asc += 6;
  return String.fromCharCode(asc);
}

function getRandomString(length) {
  var i, letters = [];
  length = parseInt(length, 10);

  for(i = 0 ; i &lt; length ; i++) {
    letters.push(getRandomLetter());
  }
  return letters.join('');
}

// this is the equivalent of original function
function getCustomRandomString(separator, min, max, style) {
  var string = getRandomString(getRandomInt(min, max));

  if(style === 'upper') {
    string = string.toUpperCase();
  } else if(style != 'both') {
    string = string.toLowerCase();
  }

  if(separator) {
    string = string.split('').join(separator);
  }

  return string;
}