On the first page of The Westing Game the reader is alerted that Barney Northrup is not what he appears to be:

Then one day (it happened to be the Fourth of July), a most uncommon-looking delivery boy rode around town slipping letters under the doors of the chosen tenants-to-be.  The letters were signed Barney Northrup.
     The delivery booy was sixty-two years old, and there was no such person as Barney Northrup. (1)

Turtle finds out later that Barney Northrup, the somewhat shady real estate agent who gets all the heirs of Sam Westing's will to live together in Sunset Towers, is really one of the many disguises of the decidely not-dead Sam Westing.  All his aliases include a compass direction:

Why did Sam Westing have to play two roles, Turtle wondered.  He had a big enough part as the doorman without playing the real-estate man as well.  Why two roles?  No, not two, three.  Windy Windkloppel took three names; one: Samuel W. Westing, two: Barney Northrup, three: Sandy McSouthers. (170)

Sam Westing's other aliases melt away, of course, and he "dies" as Sandy McSouthers.  But he does not actually die, as Turtle finds out later; he lives out his days under his fourth alias: Julian Eastman.

Now she was on her way to meet the fourth identity of Windy Winkloppel.  She could probably have figured out the address, too, instead of looking it up in the Westingtown phone book -- there it was, number four Sunrise Lane.  ... Julian R. Eastman rose.... He was smiling.  He wasn't angry with her, he was smiling.
     "Hi Sandy," Turtle said.  "I won." (174-5)

The unusual thing about Barney Northrup is that he is really Sam Westing, a man who is supposed to be dead!  Barney wasn't real; he was a disguise invented by Sam to gather his heirs together to play the Westing Game.

Source: Raskin, Ellen.  The Westing Game.  New York: Avon Books, 1978.

In Ellen Raskin's The Westing Game, what was unusual about Barney Northup,the delivery man?

Well, one could conclude that the most unusual things about the character of Barney Northrup in Ellen Raskin’s novel The Westing Game is the fact that he doesn’t exist.  It states in the book’s opening paragraph:

“Then one day (it happened to be the Fourth of July), a most uncommon-looking delivery boy rode around town slipping letters under the doors of the chosen tenants-to-be. The letters were signed Barney Northrup. The delivery boy was sixty-two years old, and there was no such person as Barney Northrup.”

“Barney” has systematically delivered six letters to six different people and, posing as a real estate salesman.  Each of these six people, presumably prospective buyers of apartments in a new, upscale building, have been selected for a reason that will become apparent as Raskin’s mystery novel progresses.  What is immediately clear, though, is that Barney Northrup, whoever he is, is a peculiar individual.  Showing the Wexlers around a unit in the newly-built complex, he displays marked enthusiasm and more than a few idiosyncrasies, as in the following passage:

“See those chandeliers? Crystal!” Barney Northrup said, slicking his black moustache and straightening his handpainted tie in the lobby’s mirrored wall. “How about this carpeting? Three inches thick!”

Another major clue that something is amiss and that Barney Northrup is an integral component of a wider mystery is revealed as he continues to show this couple around the apartment:

“’Let me remind you,’ Barney Northrup said, ‘the rent here is cheaper than what your old house costs in upkeep.’

“How would he know that, Jake wondered.”

Barney Northrup is a curious individual because, as will be revealed, he is but one of four alternate personalities of Sam Westing, and only the more perceptive of readers will notice the pattern among characters’ names, as in “Northrup,” “Westing,” “Eastman,” and “McSouthers.”  Each of these four names are points on a compass, and Sam Westing has been playing a game to determine the most worthy of heirs to his fortune.