Which quadrilateral can have 2 pairs of parallel sides, all sides with equal length, and no right angles?
A square

A triangle

A Rhombus

Trapezoic

Parallelogram is the word that most generally describes such a figure. A square or rectangle, which do, of course have right angles, are special cases of the parallelogram.

I am assuming (perhaps unjustifiably) that when you say “two pairs of parallel sides” you are talking of a figure with no other sides than those four.
There are, of course, many other polygons (hexagons, octagons, decagons, etc) which have two pairs of parallel sides and other sides, any two of which may or may not be parallel.

The attached figure is a parallelogram with one corner chopped off, making it a pentagon. It still has two pairs of parallel sides & no right angles.