Kids today just can’t bare to declare something. That’s what the grammarians tell me. (We must, of course, ignore the decisiveness of a “no!” from kids asked if they want to play outside instead of in front of the Wii, which must be some sort of anomaly from these grammatic vacillators that are our youth.) Obviously, I am far too intimidated by the wilding of American youngsters to approach one of them and listen to its speech, so I am trusting that this is a well-researched opinion and not just some made-up rubbish like the rest of the grammarians’ claims.
The key feature that sets apart those who have the conviction necessary to say what they mean and the sort of unwashed masses who kinda can’t, like, just say something is the use of qualifying phrases like kind of, sort of, and like. (I’m going to ignore like because it is far too multi-faceted for the present post.) These qualifiers are perceived as recent bastardizations of proper English, used by the kids and the cool to sorta stick it to oldsters who are so uptight and categorical. You can tell they must be recent hipster slang because they’re written as contractions without apostrophes – which is the grammar equivalent of sticking a dunce cap on a phrase and making it sit in the corner.
Now let’s pretend for a second we’re famous and well-respected grammarians – Lynne Truss, William Safire, or your own personal hero – and create a narrative that fits our beliefs that kids use kind of and sort of all the time and real grown-ups almost never use them. One possibility is that kids today are more concerned with snark than content, so you have to always hedge to avoid piddling squabbles like:
“Yo dawg, that red car over there is so the bomb.”
“Man, I don’t see no red car, but there is a slammin’ burgundy car over there.”
“Yeah, that’s the one I was talking about.”
“It’s not red, you colorblind flibbertygibbet. It’s burgundy.” (and so on…)
Compare to the obviously more genial conversation that hedges lead to:
“Yo dawg, that kinda red car over there is so the bomb.”
“Man, I think it’s more sorta burgundy.”
“It’s sorta red, kinda burgundy. Hard to say.”
“Yeah, guess so.” (handshake, or high fives exchanged in a friendly manner)
Of course, we must check to make sure that this narrative is supported by the facts of English usage. Alas, the story is — in truth — spun out of whole cloth. As it turns out, it is precisely us oldsters (or more precisely, our ancestors) who are to blame for introducing these hedges in the first place. Furthermore, the introduction of kind of and sort of proceeded by a slow, steady, — and, some hard-liners might say, pernicious — grammatical change, akin to those little puzzles where by changing one letter at a time you can convert CAT to DOG. (All credit for this is due to Whitney Tabor, who discussed this in a 1994 dissertation, and Rob Malouf, who discussed it in his book on mixed categories.)
It goes like this. You start with the undeniably grammatical construction a kind of, as in (1), where a kind of takes a noun phrase as its argument (e.g., awful torture):
(1) The trip to Irvine was a kind of awful torture.
(1′) I knowe that sorte of men ryght well [attested 1560]
This construction was in the language by Middle English, as shown by (1′). The next step (which I for one consider grammatical as well) is to let a kind of modify an adjective, yielding a sentence like (2):
(2) The trip to Irvine was a kind of fun – namely, the bad kind.
(2′) Its a fine ewnin but its a sort a caad 
This was in place in the language by the start of the 19th century, although it may have been somewhat colloquial then, and has seemed to have died out in most dialects by now. After all, it’s an unstable transition state, an adverb with an article, so it’s no surprise that people would want to stabilize it. There’s two options: either revert to an adjective, which gets us right back to square (1), or drop the article. People started to drop the article by the mid-19th century, so that a kind of, which converts an adjective (e.g., fun) to a noun phrase (a kind of fun), becomes an pure adverb that merely modifies an adjective, as in (3):
(3) The trip to Irvine was kind of fun. I did get to see the widest highway segment in the U.S.
(3′) I was kind of provoked at the way you came up 
You dang kids! Always ruining the language with your archaisms! Maybe the kids today do hedge their statements a lot, and maybe kind of and sort of are in part to blame. But they’ve got nearly two hundred years of usage by people like you and me and Dickens to draw these phrases from, and to justify their usage. So maybe everyone ought to give them a pass.
Summary: kind of and sort of aren’t new things that only kids say. They were derived over time from the unquestionably acceptable usage a kind of X, where X can be just about any noun. In their current usage, kind/sort of have been around for almost 200 years, and even back then were being written as kind o’ and kinda as well. And no less a personage than Charles Dickens (see usage 14d) used it in his writing. Perhaps they are informal, but they’re not ungrammatical.