I can think of three possible senses of "off the meter" that might account for the current popular phrase: (1) out of bounds, beyond the dial readings of a light, sound, or other type of gauge, as when the indicator arrow on a meter seems stuck at its extreme high end; (2) unregulated, as when a cab driver turns of the car's fare meter and drives for a special price or for free; (3) syncopated, so that the emphasis of the rhythm falls elsewhere than on the expected beat.
The meaning cited as possible source #1 appears in Frank Herbert, The Dragon in the Sea (1956) [compiled from snippets]:
Sparrow opened the exchange valve. Blood from Garcia's body began to flow into the unit's lead-lined storage system as the new blood was pumped into his body. Immediately, Ramsey's monitor snooper swung far right, stuck there.
"He's off the meter, skipper."
...
Ramsey fell silent, watching the monitor dial. It stayed against the right-hand pin. "I got his shots into him and took my own before you came up," said Sparrow. "We'd better check you now."
"Go ahead," said Ramsey. He held out his left arm, kept his gaze on the monitor dial. "Three changes through him by now for sure and he's still off the meter."
The meaning cited as possible source #2 appears in Jerry Oster, Sweet Justice (1985), reissued a year later as Rough Justice [compiled from snippets]:
"I asked him and he said he thought maybe, he wasn't sure, but maybe the cab was off duty — you know, had his off-duty lights on. If that's so, loo, and the cabby was heading home, he might not've logged the trip, just did it, you know, off the meter and pocketed the fare himself. When Grace and I were, you know, having that trouble, and I was moonlighting driving a cab to pay the extra rent 'cause I had my own apartment for a while along with the house, I used to do that now and then, you know, on my last trip of the night."
The meaning cited as possible source #3 appears in Michael Tenzer, Gamelan Gong Kebyar: The Art of Twentieth-Century Balinese Music (2000):
The vocabulary of stock ocak-ocakan rhythms is related to angsel rhythms, in that they play off the meter with insistent syncopation and, in dance music, are directly tied to detailed movements. Composers also invent new ones as frequently as they reuse the old.
One of the first metaphorical use of "off the meter" that a Google Books search finds is from Sean Henry, "Comic Threat," in Mother Jones magazine (November/December 1994):
It's difficult to blame them. Diana isn't the boy next door; his artistic tastes, when compared to the mainstream, are completely off the meter. Whether it's death or excrement, or simply shapes that make no sense, most of Diana's material leaves viewers wondering, "What's wrong with this kid?"
I think that this instance of "off the meter" probably derives from possible source #1 above, and I suspect that current usage derives from the same source.
Consistent with terpy's answer, the first instance of "off the meter" as a synonym for "very good, awesome, great" to appear in a Google Books search is this one, from a caption in "The Vibe Spot" in Vibe magazine (August 1998):
Throw your hands in the air if you love Enyce, Alizé, and hip hop! The Fat Black Pussycat kickoff party at the hotter-than-July Miami nightspot Liquid was off the meter!
My theory is that "the new normal" in use after 9/11 is a figurative extension of a therapeutic term referring to how grieving survivors handle the loss of a loved one. From an article in Psychology Today in 2010:
The phrase "the New Normal" is a term from the ‘grief and recovery' world that I've surprised myself by taking to heart. I don't take easily to slogans. If you come at me with something along the lines of "it's all good," I promise you I will snarl. (It's not all good. Some things are less than good. Other things are just okay. Iceberg lettuce, for example, or that brown blouse I thought I liked.) I do, however, feel right at home with diagnostic language, along with family oddities like, "If my grandmother had wheels, she'd be a streetcar." Hence, my fondness for the phrase, "New Normal."
Note that the publisher of the earliest book title cited in the question, The New Normal: How FDNY Firefighters are Rising to the Challenge of Life After September 11, is Counseling Service Unit of the FDNY, 2002.
The FDNY Foundation website describes the "Counseling Service Unit" in an article:
“The mental health of our members is of the utmost importance,” said Captain Frank Leto, the Deputy Director of the FDNY Counseling Services Unit. “Being in this department for 32 years, I know firefighters and EMTs respond to the most dangerous situations, but if they’re having a problem in their family or emotionally, that’s what can stop them in their tracks. We have to make sure that everyone is operating at their optimum level.”
In other words, this early publication with "The New Normal" in the title was published by a unit dedicated to mental health, that would have been familiar with the therapeutic term described in the Psychology Today article above, and the senses in which it was used prior to 9/11 as outlined below.
Many of the uses I found prior to 9/11 fit directly into this sense, and it doesn't seem far-fetched that the sense would lend itself to figurative extension as in "the nation is grieving," hence the explosion in use post-9/11.
Here are a few uses that appeared shortly before 2001.
She said it is her aim to turn those "co-victims" into people who can live in their "new 'normal.' You know you can't go back," to life before the murder, she said. "But that doesn't mean you can't be OK. There will be a new normal. There will be a new life."
Moving backward, there is this use from 1999 that describes its own context:
Those whose loved ones have died will never get back to what Klug calls "the old normal," that is, the way things used to be. "It's a process of moving to 'the new normal,'" he says. The new normal means new habits, new routines.
Another example is from 1996 in the U.K.
The counselors talk about something called a "new normal". The aim for survivors and relatives, they say, should not be to avoid the experience of last April but to minimise the extent to which it disrupts their lives.
Because of the frequency of pre-9/11 uses relating specifically to grieving for lost loved ones, with only occasional one-off uses that are unrelated to grief, my hypothesis is that this term from the Psychology community was adopted to describe the mass-grief of a country following a shocking loss.
Best Answer
I'm curious as to how else you would phrase "no such thing", so that it appears to you a strange enough construction as to make speaking of it's origin worth considering? It is the word no used in a normal manner, followed by the word such used in a normal manner, followed by the word thing used in a normal manner.
Such followed by thing we have from Old English "Exodus", which is believed compiled around 930-960 and composed earlier:
No followed by such depends on when you consider nan with the final consonant dropped to stop being none and start being no. The following is earlier than that, from Ælfric's "The Homilies of the Anglo-Saxon Church", and at some point in the next couple of hundred years, na would have been used even if what followed began with a vowel, and this would be closer to no than to none.
While I can't find at na swilc þing or na swylc þing or similar, I think it suffices to say that by the time no and none were separate words in our language (though their senses still overlap so that some uses of "no such things" could be "none such thing", albeit that might sound a bit archaic).
If we don't care about when no began to be separate to none, then we can find "Nán swylc" in the 8th Century "Cynewulf's Christ".
"No such thing" is just normal English words used normally, rather than an idiom as such.