Recently, I was discussing with my friend about unforgivable curses in the Harry Potter universe and we were wondering if unforgivable curses can be blocked.
There are no counter curses to block killing curse (Avada Kedavra) but it does not mean that the person at whom the curse is targeted must die.
“Not nice,” he said calmly. “Not pleasant. And there’s no counter curse. There’s no blocking it. Only one known person has ever survived it, and he’s sitting right in front of me.”
Harry felt his face redden as Moody’s eyes (both of them) looked into his own. He could feel everyone else looking around at him too. Harry stared at the blank blackboard as though fascinated by it, but not really seeing it at all...
Harry Potter and the Goblet of Fire
But there are ways in which Avada Kedavra can be blocked and there are multiple instances of it in the movie and also the book.
“No one knows why you lost your powers when you attacked me,” said Harry abruptly. “I don’t know myself. But I know why you couldn’t kill me. Because my mother died to save me. My common Muggle-born mother,” he added, shaking with suppressed rage
Riddle’s face contorted. Then he forced it into an awful smile. “So. Your mother died to save you. Yes, that’s a powerful countercharm. I can see now... there is nothing special about you, after all.
Harry Potter and the Chamber of Secrets
2. If the wands turn out to be brothers
“So what happens when a wand meets its brother?” said Sirius.
“They will not work properly against each other,” said Dumbledore. “If, however, the owners of the wands force the wands to do battle... a very rare effect will take place. One of the wands will force the other to regurgitate spells it has performed - in reverse. The most recent first... and then those which preceded it...”
Harry Potter and the Goblet of Fire
3. Using objects to block the curse
Harry had not even opened his mouth to resist; his mind was blank, his wand pointing uselessly at the floor.
But the headless golden statue of the wizard in the fountain had sprung alive, leaping from its plinth to land with a crash on the floor between Harry and Voldemort. The spell merely glanced off its chest as the statue flung out its arms to protect Harry.
Harry Potter and the Order of the Phoenix
4. Getting out of way
Bellatrix was still fighting too, fifty yards away from Voldemort, and like her master she dueled three at once: Hermione, Ginny, and Luna, all battling their hardest, but Bellatrix was equal to them, and Harry’s attention was diverted as a Killing Curse shot so close to Ginny that she missed death by an inch—
Harry Potter and the Deathly Hallows
We have seen 3 and 4 work against Crucio (Cruciatus Curse) and ideally 2 should also work but there are no canonical evidence for that. You are right about Imperio (the Imperius Curse).
While mattiav27 gave a spot-on answer regarding the books, blocking an Unforgivable Curse is one of the many things twisted in the films.
During the battle of Hogwarts, we can see Ginny blocking a Killing Curse (she "only" avoided it in the books, if memory serves me right) cast by Bellatrix Lestrange:
The description on the Harry Potter Wikia page where I took this image from says "Ginny is spared death by mere inches", but it seems to me quite obvious that Ginny blocked the curse with some kind of a magically created shield. Further, the reaction of George and Arthur behind her shows that there was some kind of an impact, which I think further confirms that the curse was indeed blocked and not just avoided.
Admittedly, it may have been a single event of a kind. At least I don't recall any other events of someone blocking a Killing (or some other Unforgivable) Curse.
According to this site:
The Killing Curse has no counter-curse or blocking spell, although the green bolt may be dodged or blocked with solid objects. For instance, Albus Dumbledore once transfigured a statue from the Fountain of Magical Brethren to shield Harry Potter from Voldemort's Killing Curse during the Battle of the Department of Mysteries. If the curse misses the victim and strikes an inanimate object instead, a small explosion at the point of impact results, which may start a fire of green flame.
See also Wikipedia.
I cannot find anything on the other two, so I guess that they cannot be blocked or avoided.
However, Imperio (mind control) can be resisted if you have enough strenght:
Resisting the Imperius Curse is possible, but extremely difficult. Only those of a particularly strong will can achieve it. Harry Potter, Barty Crouch Sr. and Barty Crouch Jr. each learned to resist the curse after being subjected to its effects.
(see the first link)