Question

What is a quadrilateral that isn't a parallelogram, rhombus, rectangle, square, trapezoid, or kite?

Answer 1

A scalene quadrilateral has no congruent or parallel sides.

For classification of quadrilaterals I recommend to look at the site
http://www.cut-the-knot.org/Curriculum/Geometry/Quadrilaterals.shtml

Explanation:

A search on the Web for "classification of quadrilaterals" leads to many useful sites that discuss different ways of classification of quadrilaterals.