There's a key difference between a null array and an empty array. This is a test for null.

int arr[] = null;
if (arr == null) {
  System.out.println("array is null");
}

"Empty" here has no official meaning. I'm choosing to define empty as having 0 elements:

arr = new int[0];
if (arr.length == 0) {
  System.out.println("array is empty");
}

An alternative definition of "empty" is if all the elements are null:

Object arr[] = new Object[10];
boolean empty = true;
for (int i=0; i<arr.length; i++) {
  if (arr[i] != null) {
    empty = false;
    break;
  }
}

or

Object arr[] = new Object[10];
boolean empty = true;
for (Object ob : arr) {
  if (ob != null) {
    empty = false;
    break;
  }
}

This sounds like a bad design to me. Null is null, empty is empty, if it's a string it's a string, and so on. Don't try to jam everything up in one method. It's bad for maintainability and readability.

if (str == null || str.isEmpty())
    ...

and

if (coll == null || coll.isEmpty())

are both perfectly fine.

Personally however, I try to never ever equate null with an empty string or empty collection. I think it's a bad practice. A null collection is no collection at all, an empty collection is in fact still a collection. You can avoid many if (coll == null) checks by keeping a collection non-null. If you're worried about memory consumption, use use Collections.emptySet et al.

That being said, if you still want to go in this direction, I'd suggest you use plain method overloading and create one isEmpty(Collection<?> coll) and one isEmpty(String str) to avoid instanceof and casting.

Regarding your edit:

Don't do for instance

if (value == null || value.isEmpty()) {
    return true;
}
return false;

just do

return value == null || value.isEmpty();

As simply as:

if (numbers.isEmpty()) {...}

Note that a quick look at the documentation would have given you that information.