Irony, satire, and sarcasm all fall into the category of, "That's funny but I'm not sure what my English teacher wants me to call it."

Irony describes situations that are strange or funny because things happen in a way that seems to be the opposite of what you expected. Note the "opposite" here. If an expectation is black, then an ironic outcome would be white, not off-white or gray. Here are some clear examples.

Bill Hillmann, the author of multiple books about how to not get gored by bulls was the only non-Spaniard to get gored in the 2014 running of the bulls in Pamplona. (Cracked Magazine July 2015)

The Business Software Alliance is an an anti-piracy agency that used to pay people to report unlicensed content on the internet. The group has been caught using a "stolen" photo in one of their ads to attract new snitches on Facebook. (Cracked Magazine July 2015)

Satire means making fun of people by imitating them in ways that expose their stupidity or flaws.

In 2000, Saturday Night Live's satire of what happened in the [presidential] campaign became the conventional wisdom for what was going on in the campaign. (The Observer)

The late-night talk and news satire is scheduled to return with new episodes in February. (Los Angeles Times)

As with satire, sarcasm depends on the listener or reader to be in on the jokeSarcasm is insincere speech. Your mom asks if you're excited to start cleaning the kitchen and you say, "Yeah, right," when you mean "Heck no." Take this exchange from The Hunger Games.

"What about you? I've seen you in the market. You can lift hundred pound bags of flour," I snap at him.
"Yes and I'm sure the arena will be full of bags of flour for me to chuck at people."

To distinguish irony from satire and sarcasm, remember that irony pertains to situations while satire and sarcasm are forms of expression. People make satire and sarcasm happen. Irony is just there.