Let it begin!!!
On the plane known as Ulgrotha, a war took place between several planeswalkers and a group of Wizards. This plane was plentiful with open space and mana. So this is where differences were sometimes settled. A planeswalker named Ravi used the Apocalypse Chime to destroy most life and mana on Ulgrotha. Afterward, 2 planeswalkers named Feroz and Serra discovered the plane and wanted to protect it from other walkers. They made a ban around the plane killing Feroz in the process and Serra soon after.
Sengir is actually a race of vampires. Baron Sengir's father was stranded after a dual between 2 planeswalkers on Ulgrotha. Baron plotted to kill his father and the child later known as Ravi. As Baron grew older, he too plotted to take over Dominaria. A race of Dwarves lived in a city beneath his Castle. Through a Dwarven Gate, the Baron could 'planeswalk' to Dominaria. As a show of force to the Dwarves, Baron actually turned the Dwarven King's daughter into a vampire. She became known a Irini Sengir.
After Ravi sounded the Apocalypse Chime, she locked herself away in a vault. Only to emerge, with Baron's help, old and bat shit mad. He brought her into the fold of his make shift 'family' and dubbed her Grandmother Sengir.
As a side note...in Time Spiral you find out because Ravi rung the Chime it ruptured the Madaran rift on Dominaria and caused it to fracture into Kamigawa, which allowed the events of Kamigawa to transpire.
The Baron has many helpers and followers. One of Baron's loyal followers is Veldrane of Sengir. Funny enough NOT a vampire but a rouge. His driving motivation was to kill Autumn Willow. She was avatar of the Great Wood of the Homelands. Originally a simple forest spirit, but strengthened by Feroz’s Ban. The Autumn Willow was the Protector of the folk of An-Havva and an enemy of Baron Sengir. After the failing of the Ban and the growing influence of the Dwarven Gate she weakened. The Dwarven city beneath Baron's Castle has a Dwarven Gate that was a artificial portal from from Ulgrotha to Dominaria.
On a card note it is rumored the Sengir Vampire was the expiration for the Baron Sengir card...
...unless they were trying to give the Baron a sex change later(no homo).
Also so with so many vampires...only 3 true werewolves have been printed.