For checking if a variable is falsey or if it has length attribute equal to zero (which for a string, means it is empty), I use:

function isEmpty(str) {
    return (!str || str.length === 0 );
}

(Note that strings aren't the only variables with a length attribute, arrays have them as well, for example.)

Alternativaly, you can use the (not so) newly optional chaining and arrow functions to simplify:

const isEmpty = (str) => (!str?.length);

It will check the length, returning undefined in case of a nullish value, without throwing an error. In the case of an empty value, zero is falsy and the result is still valid.

For checking if a variable is falsey or if the string only contains whitespace or is empty, I use:

function isBlank(str) {
    return (!str || /^\s*$/.test(str));
}

If you want, you can monkey-patch the String prototype like this:

String.prototype.isEmpty = function() {
    // This doesn't work the same way as the isEmpty function used 
    // in the first example, it will return true for strings containing only whitespace
    return (this.length === 0 || !this.trim());
};
console.log("example".isEmpty());

Note that monkey-patching built-in types are controversial, as it can break code that depends on the existing structure of built-in types, for whatever reason.

There are just a few revisions I would make.

First, always use === instead of == in Javascript. You can read more about that on Stack Overflow.

Second, since undefined is mutable, I would reccomend using

typeof value === "undefined"

instead of

value === undefined

Third, I would remove the !value and value === "" conditions. They are redundant.

My Revision

I would use a slightly different approach than you:

String.isNullOrEmpty = function(value) {
  return !(typeof value === "string" && value.length > 0);
}

This checks if the type of the value is "string" (and thus non-null and not undefined), and if it is not empty. If so, it is not null or empty.

Note that this returns true for non-string inputs, which might not be what you want if you wanted to throw an error for an unexpected input type.