Certainly, here's a Java program that checks if a string is empty or null:

public class StringChecker {
    public static void main(String[] args) {
        String str1 = "";
        String str2 = null;
        
        // Check if str1 is empty or null
        if (str1 == null || str1.isEmpty()) {
            System.out.println("str1 is either null or empty.");
        } else {
            System.out.println("str1 is not null or empty.");
        }
        
        // Check if str2 is empty or null
        if (str2 == null || str2.isEmpty()) {
            System.out.println("str2 is either null or empty.");
        } else {
            System.out.println("str2 is not null or empty.");
        }
    }
}

In this program, we first create two string variables: str1 is an empty string, and str2 is a null reference.

We then check if str1 is empty or null by using the == operator to check if it's equal to null, and calling the isEmpty method to check if it's an empty string. We do the same for str2.

The output of this program will be:

str1 is either null or empty.
str2 is either null or empty.

This indicates that both str1 and str2 are either null or empty.