Obyron is a bodyguard to Nemesor Zahndrekh, a title he earned while doing their very first campaign together, back when the Necrons were still flesh-and-blood Necrontyr. It is his job to ensure that Zahndrekh's prisoners are killed whilst 'trying to escape', among them was Illic Nightspear and Kor'sarro Khan of the White Scars.
He is also responsible for making sure the Nemesor's Royal Court is corruption-free (and by that, we mean should one of the Lords attempt to create a plan to overthrow him, Obyron simply either disposes of him by making them 'disappear' or said Lord challenges Obyron to combat and loses). The result is that in practice, Obyron is the real power in Zahndrekh's court, but he's too loyal to him to overthrow him.
Unlike the Nemesor, he has seen the changes in the Necrontyr, but all of Obyron's attempts to make Zahndrekh aware of these changes has been unsuccessful so far; Zahndrekh still believes he's in the past. So the Vargard simply just follows orders and does not ask of anything apart from continued service.
He is named for King Oberon from Renaissance literature (most famously A Midsummer Night's Dream) but this seems to have no bearing on his character.
On the Tabletop
On the table, Vargard Obyron is a force to be reckoned with; he has all the resilience of an Overlord/Lord (Sempiternal Weave bitches!), his personal weapon of choice is the same Landraider-opening Warscythe most Overlords use, and because he IS the Close Combat Lunatic he has a very high Weapon Skill. Despite Obyron's comparatively low initiative, the power weapon nerf has made him even more devastating.
His 'Cleaving Counterblow' is able to make a grand total of 9 (10 if charged or using Counter-Attack rule - Courtesy of Zahndrekh!) attacks, because of this he is likely to tear most TEQ and MEQ apart. Only working in a challenge is kind of a downer, but his ability to massacre sergeants and nobs far outweighs his points cost, and the remaining wounds after his challenger is bisected by him are carried to his unit. Obyron also has a special Veil of Darkness called the 'Ghostwalk Mantle', which operates exactly like the Veil of Darkness in the 3rd Edition (He can teleport anywhere using the Deep-Strike rule, does not also scatter if he arrives within 6" of Zahndrekh and can also teleport out of combat in his turn, rather than attack). Should Zahndrekh be in combat with an enemy unit, Obyron uses his 'Ghostwalk Mantle' to appear right next to him in combat, talk about loyal! Obyron and Zahndrek make a very statistically solid pair: Zahndrekh can tank anything capable of ignoring 2+ armor, and anything that can't is meat for Obyron. Meanwhile, Obyron is precisely the right person to benefit from Zahndrekh's buffs.
In 8th Edition
8th Edition saw a retooling of his rules. Cleaving Counterblow now means that he can keep fighting for one fight phase even if he is killed during it, all units within 6" of him can reroll morale (re-roll wound rolls of 1 in the codex), the Ghostwalk Mantle still works the same and when he's within 3" of Zahndrekh he can turn wounds on his Overlord into mortal wounds for himself on a 2+. Obyron is still a beast in combat, even with his number of attacks being gimped: 3 attacks (4 in the codex) at Strength 7 AP-4 D2 is more effective against large and tough units this time around rather than him being the horde buzzsaw of before.