Sarcasm is something said sharply or bitterly.

Cynicism is the doctrine of the Cynics.

Irony is to say something and mean the opposite.

It’s not surprising that they would be difficult to separate. Wikipedia offers this definition of sarcasm and I think you will see how it’s easily confused with irony. “Sarcasm is “a sharp, bitter, or cutting expression or remark; a bitter jibe or taunt. Though irony and understatement is usually the immediate context, most authorities sharply distinguish sarcasm from irony; however, others argue that sarcasm may or often does involve irony or employs ambivalence. Sarcasm has been suggested as a possible bullying action in some circumstances.”.

They define irony as follows: “Irony (from the Ancient Greek εἰρωνεία eirōneía, meaning dissimulation or feigned ignorance) is a rhetorical device, literary technique, or situation in which there is a sharp incongruity or discordance that goes beyond the simple and evident intention of words or actions. Ironic statements (verbal irony) typically imply a meaning in opposition to their literal meaning. A situation is often said to be ironic (situational irony) if the actions taken have an effect exactly opposite from what was intended. The discordance of verbal irony is created as a means of communication (as in art or rhetoric). Descriptions or depictions of situational ironies, whether in fiction or in non-fiction, serve a communicative function of sharpening or highlighting certain discordant features of reality.”

Cynicism is perhaps the easiest to identify as entirely separate. It is defined as:
1 — capitalized : the doctrine of the Cynics
2 — cynical attitude or quality; also : a cynical comment or act

”Cynical:”:
1 — captious, peevish
2 — having or showing the attitude or temper of a cynic: as
        a : contemptuously distrustful of human nature and motives <those cynical men who say that democracy cannot be honest and efficient — F. D. Roosevelt>
        b : based on or reflecting a belief that human conduct is motivated primarily by self-interest <a cynical ploy to win votes.

The amazing thing is that our minds are capable of separating out all three and using them in our speech and writing.

So, here’s the thing about irony: People don’t agree upon what it is, and even less upon what it isn’t. So, to sum up both perfectly and humorously the various types of irony and the arguments over it, I present to you The Oatmeal. It does a far better job than I could ever do, and a better job than all other explanations I’ve seen on the internet. Bottom line: Irony is subjective (big time), because it’s all about what is “unexpected”, and what is expected and not changes from person to person. What’s ironic for me could be totally cliche to you. This also covers sarcasm, and how it relates to irony. This comic was a huge “aha!” moment for me.

Cynicism is actually a perspective, whereas irony is a device or technique in language (and occasionally a situation), and sarcasm is a tone. Cynicism is comparable to optimism and pessimism in that they are all points of view, all perspectives, all core belief systems. Cynicism is almost a pessimism on steroids, it implies a certain jadedness and distrust of others that pessimism does not necessarily imply.

@Aethelflaed TheOatmeal.com comic says it all. Dang. Now I’m hungry instead of just befuddled. Great improvement!

Irony: The douchebag who told me to move away to the back of the bus because talking on my cell phone in the front of the bus was a crime according to state law getting penalized heavily for being caught using a cell phone while on the job some months later.

Sarcasm: When I said “I don’t know..Maybe because you think you are all-powerful and can” to the douchebag who told me to move to the back of the bus after he told me ‘Why would I make that up?” when I said that he’s bs-ing me about the state law.

Cynicism: My partner responding to the situation by saying “Guess they don’t choose busdrivers for their brains.”