If you are interested in finding out whether a variable has been declared regardless of its value, then using the in operator is the safest way to go. Consider this example:

// global scope
var theFu; // theFu has been declared, but its value is undefined
typeof theFu; // "undefined"

But this may not be the intended result for some cases, since the variable or property was declared but just not initialized. Use the in operator for a more robust check.

"theFu" in window; // true
"theFoo" in window; // false

If you are interested in knowing whether the variable hasn't been declared or has the value undefined, then use the typeof operator, which is guaranteed to return a string:

if (typeof myVar !== 'undefined')

Direct comparisons against undefined are troublesome as undefined can be overwritten.

window.undefined = "foo";
"foo" == undefined // true

As @CMS pointed out, this has been patched in ECMAScript 5th ed., and undefined is non-writable.

if (window.myVar) will also include these falsy values, so it's not very robust:

false
0
""
NaN
null
undefined

Thanks to @CMS for pointing out that your third case - if (myVariable) can also throw an error in two cases. The first is when the variable hasn't been defined which throws a ReferenceError.

// abc was never declared.
if (abc) {
    // ReferenceError: abc is not defined
} 

The other case is when the variable has been defined, but has a getter function which throws an error when invoked. For example,

// or it's a property that can throw an error
Object.defineProperty(window, "myVariable", { 
    get: function() { throw new Error("W00t?"); }, 
    set: undefined 
});
if (myVariable) {
    // Error: W00t?
}

I'm a bit confused about Javascript undefined & null.

null generally behaves similarly to other scripting languages' concepts of the out-of-band ‘null’, ‘nil’ or ‘None’ objects.

undefined, on the other hand, is a weird JavaScript quirk. It's a singleton object that represents out-of-band values, essentially a second similar-but-different null. It comes up:

1. When you call a function with fewer arguments than the arguments list in the function statement lists, the unpassed arguments are set to undefined. You can test for that with eg.:

   function dosomething(arg1, arg2) {
       if (arg2===undefined)
       arg2= DEFAULT_VALUE_FOR_ARG2;
       ...
   }
   

   With this method you can't tell the difference between dosomething(1) and dosomething(1, undefined); arg2 will be the same value in both. If you need to tell the difference you can look at arguments.length, but doing optional arguments like that isn't generally very readable.

2. When a function has no return value;, it returns undefined. There's generally no need to use such a return result.

3. When you declare a variable by having a var a statement in a block, but haven't yet assigned a value to it, it is undefined. Again, you shouldn't really ever need to rely on that.

4. The spooky typeof operator returns 'undefined' when its operand is a simple variable that does not exist, instead of throwing an error as would normally happen if you tried to refer to it. (You can also give it a simple variable wrapped in parentheses, but not a full expression involving a non-existant variable.) Not much use for that, either.

5. This is the controversial one. When you access a property of an object which doesn't exist, you don't immediately get an error like in every other language. Instead you get an undefined object. (And then when you try to use that undefined object later on in the script it'll go wrong in a weird way that's much more difficult to track down than if JavaScript had just thrown an error straight away.)

   This is often used to check for the existence of properties:

   if (o.prop!==undefined) // or often as truthiness test, if (o.prop)
      ...do something...
   

   However, because you can assign undefined like any other value:

   o.prop= undefined;
   

   that doesn't actually detect whether the property is there reliably. Better to use the in operator, which wasn't in the original Netscape version of JavaScript, but is available everywhere now:

   if ('prop' in o)
       ...
   

In summary, undefined is a JavaScript-specific mess, which confuses everyone. Apart from optional function arguments, where JS has no other more elegant mechanism, undefined should be avoided. It should never have been part of the language; null would have worked just fine for (2) and (3), and (4) is a misfeature that only exists because in the beginning JavaScript had no exceptions.

what does if (!testvar) actually do? Does it test for undefined and null or just undefined?

Such a ‘truthiness’ test checks against false, undefined, null, 0, NaN and empty strings. But in this case, yes, it is really undefined it is concerned with. IMO, it should be more explicit about that and say if (testvar!==undefined).

once a variable is defined can I clear it back to undefined (therefore deleting the variable).

You can certainly assign undefined to it, but that won't delete the variable. Only the delete object.property operator really removes things.

delete is really meant for properties rather than variables as such. Browsers will let you get away with straight delete variable, but it's not a good idea and won't work in ECMAScript Fifth Edition's strict mode. If you want to free up a reference to something so it can be garbage-collected, it would be more usual to say variable= null.

can I pass undefined as a parameter?

Yes.

undefined means a variable has been declared but has not yet been assigned a value :

var testVar;
console.log(testVar); //shows undefined
console.log(typeof testVar); //shows undefined

null is an assignment value. It can be assigned to a variable as a representation of no value :

var testVar = null;
console.log(testVar); //shows null
console.log(typeof testVar); //shows object

From the preceding examples, it is clear that undefined and null are two distinct types: undefined is a type itself (undefined) while null is an object.

Proof :

console.log(null === undefined) // false (not the same type)
console.log(null == undefined) // true (but the "same value")
console.log(null === null) // true (both type and value are the same)

and

null = 'value' // Uncaught SyntaxError: invalid assignment left-hand side
undefined = 'value' // 'value'

You can use the qualities of the abstract equality operator to do this:

if (variable == null){
    // your code here.
}

Because null == undefined is true, the above code will catch both null and undefined.

The usual way to check if the value of a property is the special value undefined, is:

if(o.myProperty === undefined) {
  alert("myProperty value is the special value `undefined`");
}

To check if an object does not actually have such a property, and will therefore return undefined by default when you try to access it:

if(!o.hasOwnProperty('myProperty')) {
  alert("myProperty does not exist");
}

To check if the value associated with an identifier is the special value undefined, or if that identifier has not been declared:

if(typeof myVariable === 'undefined') {
  alert('myVariable is either the special value `undefined`, or it has not been declared');
}

Note: this last method is the only way to refer to an undeclared identifier without an early error, which is different from having a value of undefined.

In versions of JavaScript prior to ECMAScript 5, the property named "undefined" on the global object was writeable, and therefore a simple check foo === undefined might behave unexpectedly if it had accidentally been redefined. In modern JavaScript, the property is read-only.

However, in modern JavaScript, "undefined" is not a keyword, and so variables inside functions can be named "undefined" and shadow the global property.

If you are worried about this (unlikely) edge case, you can use the void operator to get at the special undefined value itself:

if(myVariable === void 0) {
  alert("myVariable is the special value `undefined`");
}