A tough nut or a hard nut to crack is a situation, person, group, etc. which is difficult to deal with; or a place or opportunity to which it is difficult to gain entry. [wiktionary.org]

Phrases.com has a specific origin for the phrase:

This particular expression comes from 18^th when Benjamin Franklin wrote a letter to his brother. A few colonists in US were trying to attain a French Fortress somewhere in Canada in 1745. Benjamin used the following words in the letter; “fortified towns are hard nuts to crack; and your teeth have not been accustomed to it.” However, new Englanders were able to capture the fortress and thus it was proved that there are a few nuts that are much easier to be cracked.

I found no information on when or how the phrase entered popular culture, but did discover that there are other slang uses for the word “nut.” No – not the body part you’re thinking of.

[The nuts refers to] the best possible hand — is one of those great poker terms that most players learn about soon after becoming acquainted with the game… just pronouncing the word “nuts” forces the speaker to end with a smile… pokernews.com

Such a hand would be tough to crack, or win against.

Pokernews further uses a meaning of “nuts to” listed from The Oxford English Dictionary, as “a source of pleasure or delight to one.” They suggest that meaning moved into poker, where having four aces in a game of five-card draw would most certainly be “nuts to” the player holding the hand. That seems strange to me since I think of “nuts to you” as an angry retort to someone who caused upset, perhaps a euphemism for a stronger condemnation.

I was aware that the expression referred to taking a shot of booze to cure a hangover caused by that same booze. I did not know that it originated with a myth that someone bitten by a rabid dog could be cured with a potion containing some hair from that dog. The Oxford Dictionary of Word Origins warns that there is no “…scientific evidence that the cure for either a hangover or rabies actually works.

“The world is your oyster” has never been a favorite expression of mine, perhaps because oysters make me violently sick. Please world, don’t be an oyster for me, even if today the phrase means “you can have anything you want.”

The phrase “first appears in Shakespeare’s play ‘The Merry Wives of Windsor’ (1600).
Falstaff: I will not lend thee a penny.
Pistol: Why, then, the world’s mine oyster,
Which I with sword will open.’ Act II, Scene II.”

The original implication of the phrase is that Pistol is going to use violent means (sword) to steal his fortune (the pearl one finds in an oyster). English.stackexchange.com

Shmoop.com says “The subtext of Pistol threatening Falstaff is gone nowadays. There is no sword or threat in our modern version. Instead, we just like to think that if we’re persistent enough, we can find those oysters with pearls anywhere in the world.”

I didn’t see any earlier citations, so the Bard wins this phrase.

I’ve always shied away from posting this expression, believing it the origin was probably too obvious. It must, I thought, refer to the cock strutting around the barnyard and feeling important. That would translate to a person in charge of a situation behaving in the same manner. Turns out the expression began as “rule the roast.” It indeed refers to someone in charge, but the origin was the description of the person in charge of the important task of cutting the roast. The internet has all manner of explanations about the expression that I had always deemed to be to uninteresting to use as a post!

Charles Earle Funk describes this expression in his book A Hog on Ice and Other Curious Expressions. He says it originated from observation by early sailors that a turtle turned on its back is helpless and makes for an easy meal. It is natural that they would describe a ship that has been capsized as having “turned turtle.” The sailors on a ship that has been turned upside down are undoubtedly just as helpless as that turtle they intended to fix into a meal.  

I seem to have a fascination with the Spanish Civil War this week, which was when this expression was first used by Nationalist General Emilio Mola. According to Wikipedia, he told a journalist that the four columns of his soldiers marching toward Madrid would be supported by a “fifth column of supporters” inside the city. The expression began to be used to describe instances where sedition and disloyalty are feared.