There is no specific name for such a quadrilateral.
A rectangle
Trapezoid.
rhombus. The rhombus is a quadrilateral with all sides equal in length. It is also a parallelogram, so opposite sides are parallel and equal in length, and opposite angles are equal.
It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.
It's impossible for a quadrilateral to have no equal sides and have right angles.
There is no specific name for such a quadrilateral.
A rectangle
A quadrilateral with 4 equal sides and 4 right angles is a square.
Trapezoid.
A rhombus is a quadrilateral with 4 equal sides and if the angles are also all equal that that rhombus is a square.
A Rhombus has four equal sides but not (necessarily) four equal angles.
A parallelogram has opposite sides and angles congruent which means of equal measure.
rhombus. The rhombus is a quadrilateral with all sides equal in length. It is also a parallelogram, so opposite sides are parallel and equal in length, and opposite angles are equal.
It is not possible for a quadrilateral in Euclidean plane geometry to have no equal angles and still have its opposite sides parallel.It's possible for a quadrilateral to have no equal angles and two of its sides parallel (opposite ones, obviously; adjacent sides can't possibly be parallel). That would be a trapezoid.
Parallogram
Not normally