I don't understand really any of this! In Thor, Loki's eyes were green. Clearly green. But in The Avengers, they were blue. You can clearly tell. But then in Thor: The Dark World, his eyes are green again. So I have no idea.
I believe this may be an artifact of Thanos'/the Staff's control.
Here is a photo of Hawkeye towards the end of the movie (after he has been released from the staff's control):
His eyes appear to be brown.
His eyes are colored similarly in the art for Age of Ultron
And here is Hawkeye while under the control of the staff. His eyes are suddenly blue!
Erik Selvig seems to go through a similar transformation.
Marvel's official site confirms that Loki was under the effect of the scepter. It could be a weaker control, possibly explaining the lesser visual effect than the one we see on Hawkeye and Erik.
Arriving at the Sanctuary through a wormhole caused by the Bifrost, Loki met the Other, ruler of the ancient race of extraterrestrials the Chitauri, and Thanos. Offering the God of Mischief dominion over his brother’s favorite realm Earth, Thanos requested the Tesseract in return. Gifted with a Scepter that acted as a mind control device, Loki would be able to influence others. Unbeknownst to him, the Scepter was also influencing him, fueling his hatred over his brother Thor and the inhabitants of Earth.
Loki's eyes are actually blue. In the comics, Loki's eyes are green, but it is unclear in the films what eye colour Loki has because they seem to change from blue to green. However, the actor, Tom Hiddleston has addressed this question and confirmed that they are indeed blue:
"In making [Loki] with this raven black hair and blanching my face of all color, it changes my features. Suddenly my blue eyes look a lot bluer, which lends a severity to my face."
It is common for people to have eye colours that seem to change colour (found particularly in hazel eyes). Elizabeth Taylor is a good example: her eyes looked purple when they were just a deep blue. Some people who have brown hazel eyes appear to have green eyes while others may have green eyes that appear blue or vice versa. This can be caused by the clothing colours, sun exposure (aka lighting) and makeup.
As for the Tesseract theory, when you compare Hawkeye's and Dr. Erik Selvig's eyes to Loki's, you'll notice that both Hawkeye and Selvig have hardly any pupils under the power of the mind stone, while Loki does (which further proves he wasn't under its influence). So, while this theory is interesting, it most likely isn't the case.
Hmm, it's hard to say what really caused the eye color change BUT my father had hazel eyes that usually looked blue, but, when he was angry or upset, would shift to a bluish brown. (I need to point out here that no one has eyes that are only one color; the predominant color is what you see.) While my father had hazel slated towards blue, mine are blue with gold and green highlights. MOST of the time they look completely blue, but when I'm emotional or in hazy lighting they look hazel.
Personally, I think that Loki had green eyes with blue highlights that kinda swamped the green when he was not in his right mind or under another's influence--both of which happened in the first Avengers film. Poor Loki had a universe sized case of PTSD complicated by Stockholm Syndrome. No wonder his eye color shifted!
In Avengers, Loki's eyes were blue, because he, also, was under the Tesseract/Thanos' control. I'm very sure that Tom Hiddleston's eyes are blue-green, whereas Loki's (original Loki, from comics) eyes are green. So sometimes Loki's (Loki in the Movie) eyes appear green and sometimes they appear blue, but I know that in Avengers, his eyes were made blue, because of the Tesseract's control. Some people say that Marvel doesn't use contacts, but that's not true. They had to change Hawkeye/Clint Barton's eyes to blue in Avengers and also Erik Selvig's eyes. So Tom's eyes are blue-green and in Avengers his eyes were blue to show the Tesseract/Thanos' control. But, you need to remember, original Loki's eyes are actually green. Not blue-green or any in-between, just green
I believe that Loki was under Thanos' control, but instead of being mind-whammied like Barton and Selvig was, his thoughts have been influenced and warped to suit Thanos' needs. Note that in Thor 1 he said that he didn't want the throne, he only ever wanted to be Thor's equal.
At the start of the movie where he steals the tesseract, he looks very ill. I think it's because he has been tortured through heat, as he's a Frost Giant and prefers the cold. Warmer temperatures are most likely very uncomfortable for him.
In The Avengers, Banner says that you can practically smell crazy on Loki. Loki is many things, but he is not crazy. He acts with passion and intelligence. If he really wanted to invade Earth, he wouldn't have done it the way he did. He would've gotten people to trust him and worked from the inside, and when people were least expecting he'd attack.
In Thor: Ragnarok, he had the throne. But he did nothing, he only invested in theatrics and ate grapes while amusing himself through plays. He didn't do anything with malicious intent, and Asgard seemed fine under his rule. He's a sneaky bastard and no one really suspected, though I don't doubt some were suspicious of 'Odin's' behaviour.
Addition, in Infinity War, Thanos stated 'no resurrections this time'. I am going to assume that Loki died due to his fall, and Thanos found him adrift and thought hey, he's perfect to be my general, so he brought Loki back to life just to torture him further.
The info I can find points out these two key details:
After falling from the Bifrost and into the void, Loki spent a good year in the realm of Thanos, the Other, and the Chitauri. (It may have been longer, the way that Sakaar time is much longer than regular time.) Loki's actor describes it as "the seventh circle of hell," and various fic writers have taken this to mean that Loki was tortured by Thanos in much the same way as Thanos tortured Gamora and Nebula, molding them into his servants.
(I do like the idea that Thanos resurrected Loki -- that gives that line a good context. You could take the thought that Loki died in the void, Thanos revived him, and then, over a full year of torture, repeatedly brought him back to life, never letting him escape the torments. Small wonder his mind might be a little unhinged when he returns to Earth!)
The scepter definitely had an effect on Loki (that's confirmed, not speculation), though not outright control like with Hawkeye -- it was more like amplification of his negative feelings. So the motivations of Thor (desire to be valued, admired, to fit in, to prove that he's capable and not weak or stupid or unworthy; self-hatred, casting aside the "inferior" parts of himself; his self-esteem damaged through centuries of neglect and lies) would've been even greater factors than they were to begin with. Hence his lack of moderation and compassion throughout this one film, compared to any other film in the franchise.
Tom Hiddleston has the same problem. His eyes are green in some lights, grey in some and blue in some. From birth they were identified as blue.
Loki's eyes are the same as Tom's, and it is Tom's fault they seem to change because in different lights his eyes look different. Loki was under the power of the Mind Stone, but the sceptre never controlled him the way Clint and Dr Selvig were.
It's just the actor's real eyes that are confusing you all!