My take on the storyline:
First off let's start with the main character's name. It's Richard. We're introduced to Richard when he starts talking to the three masked men.
The horse represent's Richard's past.
"Oh you don't know who you are? Perhaps we should keep it that way" this is Richard being unaware of what he's done.
"But I know you." The Rooster mask which is named Richard. This represents you/the present.
"Look at my face. We've met before. Haven't we?" Yes because you're the same person.
The Owl represents Richard's future/conscience.
"I don't know you! Why are you here? You're no guest of mine!" Richard's conscience is upset with the fact that he's taken to murder.
"Do you really want me to reveal who you are? Knowing oneself means acknowledging one's actions" This is a major clue. The first part of the game is Richard's memory. You aren't present. Since this occurs before you actually murder anyone, Richard doesn't realize who he is. "As of lately, you've done some terrible things" like kill people.
"You don't remember me? I'll give you a clue. Does April 3rd mean anything to you? I believe that was the day of our first encounter. You look like you might be remembering something" Then you start.
Richard does his first mission. Which is interesting. You get your package which contains your mask and a letter. You automatically know where the drop off zone is. You've been told where it was before. That or you were hypnotized. Either way, you know. You go kill, get the briefcase and deliver it. Notice, when you're doing the killings, music is playing. This means that Richard is in his hypnotic state. Once you kill the homeless man, you're normal, old Richard. This is why he vomits after the kill. Richard as himself is not used to this.
After "saving his girlfriend", Richard consults his mind.
"Oh it's you again" says his past. Referencing that Richard is revisiting his past. "It looks like you've been busy since we last met." Busy remembering.
"I see that you remember me now. Don't you? But you still don't know who I am." Richard remembers how he began killing. But he doesn't realize where he is presently. "You don't know who introduced us, do you?" You really don't.
"Why did you come back here? You're not a nice person are you? You make me sick!" This is Richard's conscience scolding him for remembering his killings.
"A picture is starting to take form here... I wonder if it's accurate. Some pieces don't quite seem to fit. Or maybe I just don't like the way it looks." Richard's past realizes that Richard is misremembering. Or constructing his memories how HE wants. Richard DIDN'T save his girlfriend. She's dead. That's not all but we'll get to that.
"I think our time is up. But we'll meet again. Before you go, here's four questions to ponder.
Do you like hurting other people? (No. Richard is hypnotized)
Who is leaving messages on your answering machine? (We'll get to this)
Where are you right now? (Richard is in the hospital. We'll get to this)
Why are we having this conversation? (Because Richard is in a coma. This is his mind's construction to help him make sense of his world.)
That's all for now. See you soon..."
Richard then goes on to kill some more. Notice here that you start seeing other bodies who are from your organization. The men in white are the Russian mafia. In one level you see a masked man being tortured for answers, you fine one dying in the sewer (probably killed by your handlers), and one on the dance floor in one of the missions. Richard is the clean up man. He goes and does jobs that others aren't capable of.
Richard's handlers call him to deal with the problem at Phone Hom. This is where things get fucked up. Richard recalls walking into a building full of dead bodies and killing the helmet wearing man. This memory is unreliable. Afterward, Richard consults his mind. This time he is covered in blood and his mind is radically deteriorating.
"So, you came back?" asks his past. "How are you feeling? You look ill." Yes, because Richard is in the hospital. He lost that fight. "Maybe you should see a doctor?" Indeed. He needs medical attention.
"I told you not to come back here! I see that my opinion of you doesn't matter..." Richard's conscience scolds him. This is basically his conscience saying "The more you remember these events, the worse your state is... But I see that doesn't matter. Go ahead. Go psycho." He goes on "If you insist on returning here, then I should leave!" Which is Richard's conscience's way of saying "Why should I stop you from murdering people? Obviously you relish these memories!"
"Have you thought about what I asked you last time? I'm not here to give you any answers..." Richard's present says. This is because he genuinely doesn't know the answers. Not now anyways.
"Questions are all I have to offer a man like you." That's because Richard is questioning himself. That and because he is questioning the present.
"If you're not feeling well, maybe you should rest? Some thing work out best when you don't try so hard. No matter who you are, bearing too much weight inevitably leads to the collapse of everything." Richard's past is telling him to stop remembering these events. He has no real reason to. By constantly reminding himself of what he's done, he risks going psycho.
"Next time we meet will be the last." Says Richard's present self. "I can see it in your eyes." Richard is beginning to wake up. "Before you go I'll leave you with three predictions:
Someone you know is not who you think he is. (I believe this is referring to helmet guy. In other words: he's not dead. He's also not a bad guy.)
Something will soon be taken from you. (Yes, your girlfriend, your life and your sanity.)
On July the 21st you will wake up in a bigger house. (On July 21st, the mission Trauma takes place. You wake up in the hospital)
That is all"
It is after Richard's encounter with the helmet guy that he starts to hallucinate and see dead people talking. It's AFTER Trauma that the hallucinations go away. The rat is in your apartment and when you walk in you see that your girlfriend has been murdered.
"Ah, there you are! I was wondering when you'd be getting back." Richard is not under hypnosis right now. The rat is. "Well, let's get this over with then." B
Richard is shot.
Richard comes back to see his present projection sitting on the couch. The atmosphere changes to the same one as when you consult your mind other times.
"Looks like it's only you and me left now. I'm sure you know by now, that this won't end well. Soon you will be all alone. But that's okay." This is referencing the fact that Richard will wake up in the hospital without any friends. His girlfriend will have been murdered.
"Before we say goodbye, I'll let you in on a secret... What you do from here on, won't serve any purpose. You will never see the whole picture... And it's all your own fault. Now it's time for you to leave. There's a warm bed across the hall from here."
This is in reference to one of two things. You can argue that Richard died. The ending is all his imagination. But I'd like to think the game isn't THAT grim.
Richard says to himself "You'll never see the whole picture." There's one reason for that.
"And you look like you can use some rest."
Richard wakes up on July 21st. He isn't psycho. In fact, he's far from it. He's "waking up" at this point. He desperately wants answers. Having been trained to be a killing machine, Richard does what he does best, he kills all the police to get answers from the rat man. Upon being disappointed, Richard kills him.
Richard finally confronts the boss of the Russian mafia. Once killing him, Richard finally feels liberated. No longer bound to kill. He doesn't seek answers because he is satisfied. The ending is bitter sweet. Richard's life is destroyed but he is no longer a puppet. Unfortunately he'll never know the full story.
But Helmet guy, on the other hand, never fell for the tricks. While he had joined up with the same movement as Richard, Helmet guy wanted to get to the bottom of who was calling the shots and why this was happening.
Helmet guy goes to Phone Hom. Here (in my opinion. Depends on how you play/interpret it) Helmet guy DOES NOT kill anyone at Phone Hom. In fact, Helmet guy tries not to kill anyone unless they're armed. Helmet guy only kills the Phone Hom CEO cause he knows that they're the hub for where the calls are coming from.
"Interesting..." Helmet guy finds an address. "So that's where you've been hiding..." Richard walks in. Wearing the Rooster mask. This is why present projection Richard is wearing a rooster mask in the mind consultation sequences. That's what he was last wearing before the coma.
"Get out of here if you don't want to die!" Unfortunately Richard can't talk or fight it. He's hypnotized to kill everyone at the address he was given. It was Richard who killed the employees. It was Richard's mission to kill helmet guy. His fucked up memory made him remember it differently.
"Okay have it your way!" Helmet guy slices Richard. "You had your chance." Just like that, Richard is hospitalized. This is further alluded to when you play as Richard and do this mission. The bartender says "I have a feeling something terrible happened tonight... There's something in the air" this is in reference to Richard's injury.
The rat killed Richard's girlfriend.
Helmet guy hospitalized Richard.
In the end, Richard doesn't find out why these things were happening. He killed the Russian mob boss and was liberated by completing his mission rather than destroying the source.
Helmet guy DOES find the answer. He finds the base of operations in the sewer with the cleaning people. If you input the password, Helmet guy discovers that the cleaners' plan was to ruin Russia and America's relations through the destruction of the mafia.
That's it. The final conclusion of whether or not they succeed or what helmet guy and Richard do next is to be determined. Perhaps there will be a sequel or DLC!