Get any 4 sided shape and vary all the sides to different lenghts and make it look weird-there you go an irregular 4 sided shape.
A trapezium is not a regular shape although it is a 4 sided quadrilateral.
In 2 dimensions, a regular 5 sided figure is a pentagon. In 3 dimensions, there is no regular sided 5 sided figure. The tetrahedron is a regular 4 sided figure and a cube is a regular 6 sided figure.
A 4 sided quadrilateral is only a regular polygon when it is in the shape of a square