Diagonal or Just Plain Weird?

The Duden German Dictionary has the definition of the standard form of the adjective/adverb schräg as "deviating from a vertical or horizontal line at an acute or obtuse angle." With this standard meaning, schräg is usually translated into English as "diagonal" or "diagonally."

Sie lehnen den Kopf schräg nach links...

You'll turn your head diagonally to the left...

Caption 12, Nackenschmerzen - steifer Nacken

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In dem er sich senkrecht oder schräg positioniert,

By positioning itself vertically or diagonally,

lauert der Trompetenfisch seiner Beute auf.

the trumpet fish lies in wait for its prey.

Captions 47-48, Evolution - Meeresbewohner

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The second definition of schräg as a slang term is more interesting. Duden's definition describes schräg as "deviating from the norm, customary, or expected, and therefore unacceptable." In other words, "weird"—and not in a good way.

Although the German dictionary mentions that the slang usage of schräg is usually a pejorative or put-down, it does not give any examples of schräg used in a complimentary sense. In fact, the slang adjective—probably originally used as a put-down of jazz, experimental music, and modern art—eventually had its negative connotation turned on its head. By the late 1970s and early 1980s, with the advent of punk and industrial music, as well as increasingly "difficult" contemporary art, describing music or art as schräg was often meant as a compliment.

It might seem a bit tricky to tell if something somebody describes as schräg is meant as an insult or a compliment, but it's usually pretty easy to tell in context.

Alles frei nach dem Motto:

Everything freely according to the motto:

„Je schräger desto besser."

"the more eccentric, the better."

Caption 12, Auftrumpfen - Mit Kitsch und Protz

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Der war irgendwie psychisch ziemlich... schräg drauf.

Who was, in a way, quite psychologically... skewed.

-Angeschlagen.

-Damaged.

Caption 75, Sons of Sounds - Interview

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Die Kanzlerin auf einer vom schrägen Designer gepimpten Glitzer-Harley?

The Chancellor on a glittering Harley pimped out by the weird designer?

Caption 13, Stardesigner Harald Glööckler - Jetzt auch noch "Bling-Bling"-Motorräder

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Er fahre eigentlich Mercedes und kleide sich deshalb so schräg,

He actually drives a Mercedes and the reason he dresses so weirdly

weil er vor 20 Jahren Boris Blank getroffen habe.

is because he had met Boris Blank 20 years ago.

Captions 31-32, Yello-Biographie - Ein Leben für die Avantgarde

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The most common English translation of the slang meaning of schräg is "weird," but as you see above, there is a lot of latitude in translation, depending upon the context. The translation in the "Sons of Sounds" video as "skewed" is very clever, since it also acknowledges the translation of the standard meaning of schräg as "diagonal" yet still conveys the slang meaning!

Further Learning
Think of a concert or some kind of art event that you have attended that surprised you by being strange in a way that you liked. Make up a few sentences describing the event in a positive way using the slang meaning of schräg. Now think of some events you attended that were just too strange for you to like. Think up a few sentences describing these events in a negative way using schräg. Then go to to Yabla German and watch the full-length videos quoted above to get a better sense of the contexts in which schräg was used.