Olaf

Olaf lived in Sjornjost, Sweden with his lover Aud, who we know later as Anya. He was a Viking warrior who enjoyed hunting trolls and drinking at the bar. One night, he slept with a bar maid named Rannveig after he admits (far later in life) having had a great deal of mead. This affront spurred Aud to curse him by turning him into a troll, and although he initially attempted to convince his fellow villagers of his original identity, he quickly lapsed into the evil personality of a rampaging, pillaging Troll.

Olaf currently resides in an unknown alternate universe, as Willow Rosenberg attempted to send him to the Land of the Trolls, she admitted she could not be certain he reached her intended location.

Deity
There has been contention on the subject of Olaf the Troll's deity status. In preparation for the final battle with Glory, Anya offers up Olaf's hammer as a weapon which would be formidable due to the fact that it is a weapon of a God.

"...And Olaf the troll god's enchanted hammer. You wanna fight a god, use the weapon of a god."

- Anya Jenkins

This statement, paired with the obvious effectiveness of the hammer in regards to it's Godly title when Buffy uses it against glory, would lead one to believe that Olaf acquired troll-deity status at some point in his life as a troll.

It is also possible that the spell Aud performed granted the deity status in and of itself.

The spell was a combination of ingredients, the base transmogrification spell was Thornton's Hope, while the troll element was added via Eelsbane.

When a village woman sees the Troll-Olaf she yells:

"It's the largest troll I've ever seen!"

- Village Woman

From this we surmise the fact that physically, Olaf the Troll is larger than most if not all standard trolls.

Finally, his hammer is in his hand after the spell is complete, therefore one must assume it was somehow included in part as an effect of one of either Thornton's Hope or the Eelsbane.

Appearances

 * Triangle
 * Selfless