Most of the grain sacrifices are brought from wheat. The only other barley sacrifice brought is that of the sota woman suspected of adultery by her husband. Part of the omer sacrifice involved lifting it. As a rule, sacrifices involve redirecting our natural and physical powers towards holiness and service of G-d. The Shem Mishmuel refers to this with the ancient term, turning darkness into light.
Different sacrifices relate to different areas of life.
Animal sacrifices relate to the very intense area of our lusts, desires, and will. Wheat sacrifices relate to the area of intelligence and wisdom. Wheat is connected to this area, as the Sages say, a baby doesn t begin to call to his father until he starts to eat grains. Redirecting wisdom means taking natural wisdom and intelligence and redirecting it to wisdom of the Divine. Barley is considered animal feed.