Answer:
Shoguns were military dictators of Japan, who were appointed by the Emperor, but who actually enjoyed more power than the emperor.
Damyos are the equivalent of feudal lords in Medieval Europe. They were powerful individuals who controlled portions of Japanese territory, and who were loyal to the Shogun, while having a great degree of autonomy at the same time.
Samurais were the equivalent to European medieval knights. They were honor-based warriors who protected the Damyos and the Shogun in exchange for a wage, some land, and legitimacy.