The quadrilateral you are describing is known as a trapezoid (or trapezium in some countries). A trapezoid is defined as a four-sided shape (quadrilateral) that has at least one pair of parallel sides.
In the case of a trapezoid that has no right angles and no sides of the same length, we are looking at a specific type of trapezoid often referred to as an irregular trapezoid. Unlike a right trapezoid, which includes right angles, the irregular trapezoid can take on various shapes while still maintaining one set of parallel sides. The other two sides can vary in length and angle, differing from each other, thus fulfilling the condition of having no sides that are the same length.
In summary, the answer to your question is that an irregular trapezoid fits the criteria of having two parallel sides, without any right angles or equal-length sides.