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.

This question has two interpretations:

Check if the variable has a value
Check if the variable has a truthy value

The following answers both.

In JavaScript, a value could be nullish or not nullish, and a value could be falsy or truthy.
Nullish values are a proper subset of falsy values:

 ╭─ nullish ──────╮ ╭─ not nullish ─────────────────────────────────╮
┌───────────┬──────┬───────┬───┬────┬─────┬──────┬───┬─────────┬─────┐
│ undefined │ null │ false │ 0 │ "" │ ... │ true │ 1 │ "hello" │ ... │
└───────────┴──────┴───────┴───┴────┴─────┴──────┴───┴─────────┴─────┘
 ╰─ falsy ───────────────────────────────╯ ╰─ truthy ───────────────╯

Check if value is nullish (undefined or null)

Use one of the following depending on your coding style:

if (value == null)                         { /* value is nullish */ }
if (value === undefined || value === null) { /* value is nullish */ }
if (value == undefined)                    { /* value is nullish */ }
if ((value ?? null) === null)              { /* value is nullish */ }

Notes:

• The == operator works because it has a special case for null vs undefined comparison
• The === operator is more readable (opinion based), eqeqeq friendly and allows checking for undefined and null separately
• The first and third examples work identically, however the third one is rarely seen in production code
• The fourth example uses nullish coalescing operator to change nullish values to null for straight forward comparison

Check if value is not nullish

if (value != null)                         { /* value is not nullish, although it could be falsy */ }
if (value !== undefined && value !== null) { /* value is not nullish, although it could be falsy */ }
if (value != undefined)                    { /* value is not nullish, although it could be falsy */ }
if ((value ?? null) !== null)              { /* value is not nullish, although it could be falsy */ }

Check if value is falsy

Use the ! operator:

if (!value) { /* value is falsy */ }

Check if value is truthy

if (value) { /* value is truthy */ }

Data validation

The nullish, falsy and truthy checks cannot be used for data validation on their own. For example, 0 (falsy) is valid age of a person and -1 (truthy) is not. Additional logic needs to be added on case-by-case basis. Some examples:

/*
 * check if value is greater than/equal to 0
 * note that we cannot use truthy check here because 0 must be allowed
 */
[null, -1, 0, 1].forEach(num => {
  if (num != null && num >= 0) {
    console.log("%o is not nullish and greater than/equal to 0", num);
  } else {
    console.log("%o is bad", num);
  }
});

/*
 * check if value is not empty-or-whitespace string
 */
[null, "", " ", "hello"].forEach(str => {
  if (str && /\S/.test(str)) {
    console.log("%o is truthy and has non-whitespace characters", str);
  } else {
    console.log("%o is bad", str);
  }
});

/*
 * check if value is not an empty array
 * check for truthy before checking the length property
 */
[null, [], [1]].forEach(arr => {
  if (arr && arr.length) {
    console.log("%o is truthy and has one or more items", arr);
  } else {
    console.log("%o is bad", arr);
  }
});

/*
 * check if value is not an empty array
 * using optional chaining operator to make sure that the value is not nullish
 */
[null, [], [1]].forEach(arr => {
  if (arr?.length) {
    console.log("%o is not nullish and has one or more items", arr);
  } else {
    console.log("%o is bad", arr);
  }
});