Nutrient: a substance that is needed to keep a living thing alive and to help it to grow (营养物质)

a lack of essential nutrients

Plants draw minerals and other nutrients from the soil.

children suffering from a serious nutrient deficiency

Nutrition: the process by which living things receive the food necessary for them to grow and be healthy(营养过程)

advice on diet and nutrition

to study food science and nutrition

Nutrition information is now provided on the back of most food products.

the nutritional value of milk

a nutritionally balanced menu

Nutritious: (of food) very good for you; containing many of the substances which help the body to grow  

tasty and nutritious meals

Nourishment: food that is needed to stay alive, grow and stay healthy (营养食品)

Can plants obtain adequate nourishment from such poor soil?

(figurative) As a child, she was starved of intellectual nourishment.

These seeds can be a great source of nourishment to birds in winter.

Nourish：

1 ~ sb/sth： to keep a person, an animal or a plant alive and healthy with food, etc

All the children were well nourished and in good physical condition.

Most plants are nourished by water drawn up through their roots.

a lotion containing almond extract to nourish and revitalize the skin

2 ~ sth (formal) to allow a feeling, an idea, etc. to develop or grow stronger

By investing in education, we nourish the talents of our children.

There were hopes that the talks would nourish the fragile growth of good relations between the two countries. 

Nourishing food = Nutritious food

Malnourished: in bad health because of a lack of food or a lack of the right type of food

Tired, malnourished people are prone to infection.

Malnutrition: a poor contition of health caused by a lack of food or a lack of the right type of food