A month or so ago I started getting seemingly random notifications from the Facebook app about posts/links/photos friends had posted. The weird thing was that it wasn’t recent stuff: most of it was from several days to weeks in the past.
Here’s how to switch it off.
Go to your Account Settings
Open Notifications Settings
Open Mobile Push Settings
Un-check ‘Activity you’ve missed’
And that should be it. No more alerts informing you that that girl you worked with four years ago is “huvin a gless u vino lol”.