Okay, let me give you a hint to help you with your home work. Loading the complete file into memory will -as you know- not work, because it is given as a precondition of the assignment. You need to find a way to lazily load the data from disk as you go and throw as much data away as soon as possible. Because single lines could be too big, you will have to do this one char at a time.
Try creating a class that represents an abstraction over a line, for instance by wrapping the starting index and ending index of that line. When you let this class implement IComparable<T> it allows you to sort that line with other lines. Again, the trick is to be able to read characters from the file one at a time. You will need to work with Streams (File.Open) directly.
When you do this, you will be able to write your application code like this:
List<FileLine> lines = GetLines("fileToSort.dat");
lines.Sort();
foreach (var line in lines)
{
line.AppendToFile("sortedFile.dat");
}
Your task will be to implement GetLines(string path) and create the FileLine class.
Note that I assume that the actual number of lines will be small enough that the List<FileLine> will fit into memory (which means an approximate maximum of 40,000,000 lines). If the amount of lines can be higher, you would even need a more flexible approach, but since you are talking about 20 to 30 lines, this should not be a problem.