I've known a few senior leaders in passing I would consider oddballs, but more due to strange appearance traits and the assumption this points toward other oddball behavior, rather than an intimate exposure to one of this strange variety of leaders. Describing the oddball, therefore, is a bit more difficult for me, and I may get a few bits slightly off. So with that disclaimer in mind, here goes....
The oddball is an offbeat leader -- one who seems to be at least somewhat out of touch with the rest of his or her management team. He might range anywhere from amusingly eccentric to downright bizarre. Oddballs are often superstitious or ritual driven, as if following an old and beloved formula will lead to continuing success, even though circumstance may have changed -- a little akin to the star athlete who rubs their lucky baseball before each inning, or who always wears green underwear, or some other seemingly disconnected behavior.
Oddballs seem to love old, outdated management fads -- remember "management by walking around", "In search of excellence", Theory X, and other management theories that have faded into the past -- they live again in the Oddball's organization.
What makes an Oddball? Some simply seem to be different at their core. Most seem to have a tough time separating luck (and luck plays a role in the career of every top manager) from actual actions resulting in success.
The biggest negative impact on the organization is the tremendous waste of energy on practices, systems, analysis and other elements of the Oddball's management mantra that have little to nothing to do with the organization's success. This can range from annoying or confusing, to downright deadly, depending on the nature of the rituals, and what elements of current reality they tend to ignore.
Having an oddball for your leader can also be...well, embarrassing. Image conscious executives will stay away just to avoid the guilt by association.
