Una desairada situación o una situación desairada

Una desairada situación o una situación desairada
 

For "an awkward situation" it seems to me like the adjective ought to go afterwards, but I've seen it placed in front of the noun. Which is right?

Both locations are correct. The leading position adds emphasis to the awkwardness.

I agree with Rusty, but "desairada" sounds strange to me.

The most common meaning of "desairado", is closer to "despised".

In an infrequent use, it may mean "lackluster", and also means "awkward", but like when talking about a clumsy or graceless person.

I would prefer "una situación incómoda/embarazosa/difícil". :)

una situación incómoda (uncomfortably awkward)
una situación difícil
una situación rara (embarrassingly awkward)

In this case, we don't use an adjective+noun order unless we're qualifying a situation which has been already described:

La situación fue así ... así ... y así .... Esa incomoda situación condujo a que ...

Remember that the order adjective+noun in Spanish speaks of "the whole of it" leaving other possibilities out

la incomoda situación = una situación indudablemente incómoda

That is the best advice I have heard yet on the subject. Many thanks!