How is an overloaded method chosen when a parameter is the literal null value?

Is null a String variable pointing to nothing ?

A null reference can be converted to an expression of any class type. So in the case of String, this is fine:

String x = null;

The String overload here is chosen because the Java compiler picks the most specific overload, as per section 15.12.2.5 of the JLS. In particular:

The informal intuition is that one method is more specific than another if any invocation handled by the first method could be passed on to the other one without a compile-time type error.

In your second case, both methods are still applicable, but neither String nor StringBuffer is more specific than the other, therefore neither method is more specific than the other, hence the compiler error.

Additionally, the JLS 3.10.7 also declares that "null" is a literal value of the "null type". Therefore there exists a type called "null".

Later, the JLS 4.1 states that there exists a null type of which is impossible to declare variables, but you can use it through the null literal only. Later it says:

The null reference can always undergo a widening reference conversion to any reference type.

Why the compiler chooses to widen it to String might well be explained in Jon's answer.

You can assign a string to a null value so it is valid and the order for java and most programming languages is fit to the closest type and then to object.