Two or more organs working together in the execution of a specific body function form an organ system, also called a biological system or body system. The functions of organ systems often share significant overlap. For instance, the nervous and endocrine system both operate via a shared organ, the hypothalamus.
So, is the spinal cord an organ?
Yes, it is part of an Organ System called the Nervous System. It includes the Brain, Spinal Cord, and all the Peripheral and Cranial Nerves.
Is a nerve an organ?
The hierarchy works like this: cells make up tissues, tissues form organs, and these in turn give rise to organ systems. The liver itself is a part of the digestive system. In answer to your question, a nerve is formed of nervous tissue that is a past of the central nervous system, of which the brain is an organ.