Well, despite what Haneke says, I don't really find Funny Games to be a stern talking-to directed at violence-loving audiences. Violent anti-violence movies have a tendency to get off their leash and scamper away from their makers' intentions. Exhibit A: Natural Born Killers.
I think its target goes deeper (or wider, or whatever): It essentially attacks the audience's desire to get anything from a movie. If Haneke made a slapstick film in this mode, you'd see all the pies neatly arranged on a table but nobody would ever get hit with one. Banana peels would litter the floor, but nobody would slip on one. In this case, Haneke makes a thriller, because he knows that will hold our attention, and then meticulously goes about removing every trope that would make it cathartic. Actually, going back to the slapstick example, you wouldn't actually see someone slip on a banana peel but you would spend an entire unbroken reel with them in the emergency room as they got their scalp stitched up from the fall they took. This goes back to the classic Mad parody of Bringing Up Father, in which cartoony depictions of Jiggs being hit with dishes and lamps were intercut with bleak Bernard Krigstein drawings of what actual effect those flying objects would have (knocked-out teeth, scalp lacerations, etc.). Haneke's approach isn't new but it is, as they say, updated for the video age. It's pitch-dark Juvenalian satire.
It's very much a meta-movie, announcing loudly at several points that it is a movie, that it is fiction. That's why I called it an essay on torture porn rather than the thing itself. But whether or not Haneke after the fact wants to describe it as an annihilating frown pointed at Eli Roth fans, it really works more as a general deconstruction of what exactly we want movies, or fiction, to do. We say we want to be surprised by movies, but really we don't. We want what we want. When something new comes along we reject it. When something breaks or disregards the rules we reject it, unless it's wrapped in other comforting tropes, as in Tarantino. (Not a criticism of Tarantino, by the way: he knows and loves the rules, which is why he can toy with them so well. Same reason Trey Parker can so devastatingly write parodic musical numbers, because he's actually a huge musical geek.) Anyway, it seems like if you look at Funny Games as an overall study of why we want/need certain tropes to be observed in fiction, rather than as a specific spanking to fans of violent films, it makes more sense.
As to The Strangers, the rules it plays by are a little different because the genre is more horror than thriller. The beats are different, the tone is different. It's hard to describe, but the atmosphere is so doomy and heavy that you don't feel there's much chance of escape, something like House of 1000 Corpses. Anyway, The Strangers is problematic and thin, more of a director's calling card than a storytelling triumph: sparsely imagined but skillfully made. It's not really seeking to subvert expectations other than the basic one that the protagonists will live. It's not really working the same side of the street as Funny Games or, for that matter, Psycho. It's like a lot of other horror films where everything goes to shit and nobody lives.