Method 4 is best.

if(foo != null && foo.bar()) {
   someStuff();
}

will use short-circuit evaluation, meaning it ends if the first condition of a logical AND is false.

Checking for null is done via if (string != null)

If you want to check if its null or empty - you'd need if (string != null && !string.isEmpty())

I prefer to use commons-lang StringUtils.isNotEmpty(..)

The dilemma

If a variable with null value gets used in your program causing a NullPointerException, this is clearly a situation in your program which you did not expect. You must ask yourself the question: "Did I not expect it because I didn't take into consideration the possibility of a null value or did I assume the value could never be null here?"

If the answer is the latter, the problem isn't because you didn't handle the null value. The problem happened earlier, and you're only seeing the consequence of that error on the particular line it's used. In this case, simply adding a if (variable != null) isn't going to cut it. You'll wind up skipping lines you were supposed to execute because the variable was null, and you'll ultimately hit a line further on where you again assumed it wouldn't be null.

When null should be used

As a general rule, return null only when "absent" is a possible return value. In other words, your data layer may search for a record with a specific id. If that record isn't found, you can either throw an exception or simply return null. You may do either, but I prefer not to throw exceptions in situations where the strong possibility exists. So you return null instead of a value.

The caller of this method, presumably written by you, knows the possibility exists that the record may not exist and checks for null accordingly. There is nothing wrong with this in this case, though you should handle this possibility as soon as possible as otherwise everywhere in your program you will need to deal with the possibility of a null value.

Conclusion

In other words, treat null as a legitimate value, but deal with it immediately rather than wait. Ideally in your program, you should ever only have to check if it is null once in your program and only in the place where such a null value is handled.

For every value you expect to be non-null, you need not add a check. If it is null, accept that there is an error in your program when it was instantiated. In essence, favor fail fast over fail safe.

Your solution is very smart. The problem I see is the fact that you don't know why you got a null? Was it because the house had no rooms? Was it becuase the town had no houses? Was it because the country had no towns? Was it because there was a null in the 0 position of the collection because of an error even when there are houses in positions 1 and greater?

If you make extensibe use of the NonPE class, you will have serious debugging problems. I think it is better to know where exactly the chain is broken than to silently get a null that could be hiding a deeper error.

Also this violates the Law of Demeter: country.getTown().getHouses().get(0).getLivingRoom(). More often than not, violating some good principle makes you have to implement unorthodox solutions to solve the problem caused by violating such principle.

My recommendation is that you use it with caution and try solve the design flaw that makes you have to incur in the train wreck antipattern (so you don't have to use NonPE everywhere). Otherwise you may have bugs that will be hard to detect.

public static <T> T ifNull(T toCheck, T ifNull) {
    if (toCheck == null) {
           return ifNull;
    }
    return toCheck;
}