What systems in the body are affected by the nervous system to keep them running effectively in response to external influences?

It is only a slight exaggeration to say "all of them". The nervous system evolved originally for this function of regulating body systems, and only hundreds of millions of years later did it get co-opted into forming a brain for intelligent behavior. The nervous system regulates heartbeat, breathing, temperature through panting, sweating, or shivering, pupil dilation, hormones, blood sugar, and even the functioning of the kidneys and the gastrointestinal tract.Most of this regulation of...

It is only a slight exaggeration to say "all of them". The nervous system evolved originally for this function of regulating body systems, and only hundreds of millions of years later did it get co-opted into forming a brain for intelligent behavior.

The nervous system regulates heartbeat, breathing, temperature through panting, sweating, or shivering, pupil dilation, hormones, blood sugar, and even the functioning of the kidneys and the gastrointestinal tract.

Most of this regulation of various organs is done by the autonomic nervous system, which is primarily based in the spinal cord.

The functions of the autonomic nervous system are not under conscious control most of the time. We do have a limited amount of conscious control over some autonomic functions, and training can make people better at it, so that for example some people can hold their breath for a long time or slow down their heartbeat substantially. But the vast majority of the time, the autonomic nervous system is busy regulating our body to maintain homeostasis--conditions of roughly constant temperature and chemical distribution that are optimal for our cells and organs to function. You can think of it as falling back to a default setting when we aren't asserting control; this is why you can hold your breath if you want to, but you never just forget to breathe.

The autonomic nervous system is divided into two broad subsystems, the sympathetic system and the parasympathetic system. The sympathetic system is a stress response system evolved to make us more effective at "fight or flight"; the parasympathetic system is the counterpart that maintains our equilibrium when we are not under stress.

The liver actually has its own subsystem of the nervous system, the hepatic nervous system, which is not well understood. (The best article I could find on it was in fact published in a medical journal, so I apologize if it's too technical). We are still in the process of discovering some of the complex and subtle ways that the nervous system exerts control over the rest of the body.