A four sided figure with four equal sides and no right angles is a diamond, or a rhombus. If it had four right angles, it would be a square.
A square
A four-sided figure with no equal sides is an irregular quadrilateral.
Square
Trapezoid
A trapezium is a four sided figure with 2 sides parallel. None of its sides need to be equal in length.
A non-descript four sided figure is a quadrilateral.
Rhombus(diamond)
A Rhombus
-- trapezoid -- kite -- four-sided figure with no two equal sides
A square.
A four sided figure with no parallel sides is a trapezium, but it is also an irregular four-sided polygon, tetragon, quadrilateral, or quadrangle.