Weird polygons can happen during GIS data creation when nodes marking the perimeter of a polygon are digitized out of order in a way that creates an intersection of lines. The straightforward definition of a weird polygon is a data feature that is missing nodes. One way this happens is when the polygon is digitized in such a way that one arc cross another arc. While the end feature looks like two polygons, the cross lines are not connected by a node.
A second way weird polygons can happen is when a digitized line feature is cross over upon itself. As with the first example, the resulting digitization error makes it appear as if the feature is a polygon but the intersecting lines are missing a node.