Strings can be either primitive or objects, depending on how they were declared.
var str = 'yes';
Gives you a primitive, while,
var str = new String('yes');
will give you a String object.
All arrays are the same (Whether or not they were defined with [] or new Array()), are of the type object and inherit from the "Array" object's prototype. There aren't real classes in Javascript, everything is an object, and there's a system defined object called Array. It has a property called 'prototype' (of type object), and when you use the new keyword on an object with a prototype property, it creates an instance with a reference to the contents of the prototype and stores it in your variable. So all arrays you've ever used in Javascript are objects and instances of Array's prototype property.
In any case, although arrays really are objects, they behave like arrays because of their useful properties and functions (Such as length, slice, push etc).
Another note, although I said there are no classes, when you do this:
console.log(Object.prototype.toString.call(your_object));
it will give you a string in the form [object Object]. But what's useful is that when you call it with an array, you get [object Array] same with functions which give [object Function] and a number of other system defined types, which assists in differentiating between normal objects and arrays (Since the typeof operator will always just return the string 'object').
Try this
var a = Array;
and go into firebug and examine the contents of a, especially it's 'prototype' property.
Edit: Changed the wording a bit, to be more correct. In fact when you use the new keyword, it creates an instance which references the prototype object. So any changes made to the prototype after the instance's declaration, will still affect the instance.
Edit: In answer to your latest revised question (are arrays/objects actually strings in disguise): No. They are objects, as I've explained. Strings are either a primitive type, or an object type (An instance of the String object) which contains the primitive equivalent as one of it's properties.