If you drink a shot every time the director and screenwriters swipe from another, better supernatural horror film, you may be dead by the second hour of The Conjuring 2. Everything from the basement in Evil Dead 2 to the Danny-throws-a-rubber-ball scene in The Shining shows up. The Amityville Horror itself occupies part of the film's first act, with the Warrens debunking the debunkers who dare to challenge the veracity of The Amityville Horror, one of roughly a million 'real-life' hauntings the Warrens 'investigated' over the years.
Then we're in Merrie Olde Englande in the 1970's. The Warrens ostensibly operate as stealth agents for The Church (it's not named, but simply strongly hinted to be the Roman Catholic Church) as they investigate The Enfield Haunting. See, the Vatican relies on the Warrens to vet supernatural occurrences before sending in their exorcists so as to avoid public embarrassment should the Church accidentally try to exorcise a demon who doesn't actually exist. What, you say? Yes! No, seriously, what???????
So some 12-year-old girl gets punished for holding her friend's cigarette by having the forces of Hell unleashed on her and her family. No, that's really how the plot works in its depiction of supernatural cause-and-effect. A lot of rote supernatural stuff happens. A reel-to-reel recorder plays a key part, as does some demonology that seems... goofy. People who debunk psychic and supernatural phenomena are the secret monsters of the narrative: how dare they point out moments of clear fakery! Oh, the temerity of these godless atheists!
Anyway, it's a shitty film made by dunderheads that plays to an audience of brain-damaged Christians and fellow travelers with its Christian iconography and utterly debased and impoverished version of Catholicism. Of course it made money. Not recommended.