In the Avengers, why does Thor desperately try to break out of the cage / box while it is falling in which he is trapped by Loki if he is a demi god and immortal? I remember Loki telling him that they both are immortals and hence cannot be killed by humans.
I have not seen Thor - just Avengers - so I might have missed some back-story to this answer.
I believe he would survive, it could have been just reaction lead by fear and panic.
Loki didn't count that it would kill him, his goal was just to get rid of Thor and separate avengers. Also if Thor broke the glass earlier he could have flown back to the ship.
I believe there was a phrase something along the lines of "They believe us to be immortal" which implied to me that this was incorrect and Loki knew that the fall would indeed kill him (and Thor).
They are not immortal. Human weaponry cannot kill them due to their GOD-LIKE power, but a fall like that would most definitely. Loki is a Jotan and Thor are is an Asguardian, beings who had come to Earth during the Viking age. The Vikings mistook them for Gods and so the legend of Norse Gods was born.
(NOTE this refers to the mythical world of the Avengers and Thor. This is not a judgement on the Norse religion.)
Thor would likely die or at least be severely hurt, and they are not immortal. The idea that they are immortal comes from human Norse mythology.
Why was Thor afraid of being trapped in the cage, and why did Nick Fury put Loki in the same cage? It's because the Hulk is the only known superhero to best an Asgardian. There are several comic books, television shows and even in the Avengers films where the Hulk beats up an Asgardian.
In one Marvel animated film Loki uses mind control over the Hulk, and uses him to attack Asgard. Where the Hulk destroys most of the city before Thor is able to break the mind control spell that Loki was using, but at one point in the film Thor tells another Asgardian that he expects to die when he faces the Hulk.
In the Marvel animated film Planet Hulk. The Hulk is outcast to another planet where he battles Beta Ray Bill. Beta Ray Bill is the only other character to ever receive his own Asgardian hammer of the Gods. The same weapon used by Thor. Beta Ray Bill is the only character to match Thor's strength and good will. Still, Hulk beats Beta Ray Bill to an inch of his life before he finally stops.
In the Avengers film Hulk beats up Thor, and would have won had a fighter jet not distracted him.
Loki traps Thor in the cage, because he does not know if Thor could get out. The cage can be ejected from the carrier, because Nick Fury knows it wouldn't hold the hulk. So it's not an indestructible cage. When the cage is ejected Thor struggles to get out, and at the last second manages to escape but is knocked out in the process.
Could it have killed him? Yes. Would it be guaranteed to kill him? No, but you if want to kill an Asgard. Send the Hulk after them.
Loki was being sarcastic you see if Thor fell he would not die but be injured (as you would be after such a big fall) causing him to dissappear for a while to recover. If he was away for a while people would give up the idea of him being immortal and think he just died.
There are many good answers on the kill or injure topic so I would not say anything more about that.
But there is another aspect of the situation. Loki is free and Thor is trapped inside a glass cage. This situation is unacceptable to Thor even if he was not falling 35000 feet to the ground simply because Thor wants to stop Loki from hurting his friends and the planet under his protection. He can't do that from inside the cage.
Just my 2 cents.
Thor is not immortal and neither is Loki, otherwise there would be little point in them fighting. Loki stabs Thor and he is clearly injured from it. They are very tough compared to humans but they are not all powerful.
The fall would most likely have killed Thor - even if not it would have badly hurt him - even if not, he is not going to hang around to find out!
Thor is not immortal, just superhumanly strong. He can still be hurt and die. Loki says:
The humans think us immortal. Should we test that?
He's talking about the human belief that Asgardians are the literal Norse Gods and have the immortality associated with it. In the MCU, the Asgardians are just sufficiently advanced aliens.
The reason Thor attempts to break out of the cage are twofold. One, he wants to get back to the fight as soon as possible. Loki's still messing around on the helicarrier. Two, falling straight down at terminal velocity from miles above the Earth will hurt.
Guessing Thor is 400 lbs (Super Dense Muscle), falling from a height of 35,000 ft, and going only 0.1m into the ground, would result in 162,196,272 newtons of energy. Converted into Pounds per Square Inch, that's 23,524 PSI in a fraction of a second. Yay physics. The human body at sea level experiences 14 PSI, and can survive up to 400 PSI if slowly increased. Sudden increases are deadly. An increase of 30 PSI in a fraction of a second will kill you. A standard US military hand grenade of 0.4 pounds of TNT worth of explosives provides 836,800 newtons of energy or 121 PSI at it's source.
That means the crash of the cage would have been extremely powerful. By breaking out and redirecting his momentum sideways, Thor would reduce the amount of energy relative to the Earth (like the International Space Station does resulting in microgravity "Zero G"). Notice that Thor is still thrown around wildly, but alive.
Keep in mind, the actual force of the impact would be alot higher, as the weight of the cage was not taken into consideration.
You mentioned Thor is immortal. However Loki doesn't say he is immortal, he says the humans believe him to be immortal (link starts video at the scene I mentioned. bad quality though):
Also in Thor: The Dark World Loki (now a prisoner) and Odin have a chat about Loki's birthright that touches on their lifecycle. They live a long time but do die (scene from Thor: the Dark World):
So that is the story in the MCU. Basically Thor tried to get out because while the fall from the helicarrier wouldn't necessarily have killed him, he can die and it sure would have hurt.
They're not immortal, they can be killed, and even die of old age. But they leave much longer than human. Olympian gods, at the opposite, don't die of old age (but can be killed too).
