According to Gary Gygax, he used Potions of Longevity
The actual Mordenkainen was played as a player character by Gary using OD&D/AD&D 1e rules, to somewhere in the mid 20th levels (in this edition there was no level cap for humans). When he was ousted from TSR, Gary lost the intellectual property rights to the character, so from that point on, official canon was up to TSR and later WotC, and this answer hence does not represent canon for 5e. However, it tells you what the method originally was, in reality.
Gary shared which method he used to extend Mordenkainen's lifespan, in a Forum post on Dragonsfoot:
I envisaged Mordenkainen as around 30 year of age when he began adventuring, so that would make him around 80 years of age now (considering campaign time)--although he has quaffed a number of potions of longevity preiodically [sic], always when a wish was cast, so likely he appears more like a vigorous 50.
He does not plan to remain as a lich, not at all his style.
Potions of longevity are a risky method, as eventually they will fail and undo all the effect they had. At least, the 1e version Gary used had a much lower risk than the 5e version (1e DMG p 126):
Longevity: The longevity potion reduces the character’s game age by from 1-12 years when it is imbibed, but each time one is drunk there is a 1% cumulative chance that it will have the effect of reversing all age removal from previously consumed longevity potions. The potion otherwise restores youth and vigor.
So on average, you will get back 6-7 years whenever you drink one, meaning to appear 50 when you are 80 you would have had to drink about 5 of them - a 14% chance overall for it to fail at some point, which apparently did not happen.
Clearly, this method would be a bad gamble to get you to an age of 212 years, even using the old potion rules. With a life expectancy of about 100 years for a normal human, you would need about 17 potions, and would have only about 2% chance to survive it. So the Mordenkainen in CoS must have added one of the other methods mentioned to his arsenal.
From his comment, methods to turn him undead would be unlikely. His stats in Curse of Strahd use the normal CN male human archmage stat block with a slightly altered spell list, and the added power to grant charm of heroism. That means according to the official rules, he is not undead, he is not divine, and he does not have access to epic level spells.
The historical Mordenkainen had a variety of magic items, standouts among them were a Staff of Power, a Ring of X-Ray Vision, an Onyx Dog (which lead to the spell Mordenkainen's Faithful Hound), Bracers of Armor, the Iron Bands of Bilaro and a set of 12 different Ioun Stones. None of them would explain his unusual longevity.