OK, here we go!
Dressed to Kill: I'm almost wondering if this one has something to do with Greek tragedy, with the murder of Agamemnon by his wife Clytemenestra. Their son, Orestes, would ultimately end up murdering Clytemenestra, and maybe she realized this was possible and worried about it. I could be totally wrong about a connection, but that's just what came to mind.
Incantations of the Apprentice: This seems like a reference to The Master's Apprentice. You know...the symphony you all saw when you were little set to the images of Mickey Mouse and so on. Except this is a much, MUCH darker version of it where things do not work out so well in the end, and what the apprentice unleashes is completely uncontrollable and goes out to wreak havoc on a grand scale.
Awakenings: This one seems to me to be about an older man who has realized he's wasted his life, so at this late stage he's searching for direction and has a tough time even attending to the simple things in his life, because it seems empty and purposeless to him now.
Out of the Ashes: I might be way off base with this one, but this is a song I felt like I understood from the first time I ever read the lyrics. It seems to me almost like a young man who was beaten both verbally and physically by his father when he was growing up. In some ways he can feel the same evil in him (and maybe he's started to get out of control somewhat), perhaps because no one was there to show him a better way when he was young. But as a man he understands there was something wrong and he wants to learn more about what the right way is. He wants to put his life back together.
Church of the Machine: If I were to sum this up in two words--idol worship. Specifically, man worshipping things that he has created. This can range from worshipping material objects to worship of science, to man worshipping himself or even a distorted, self-serving image of what God really is. All of these different elements seem to show up here, and what ends up happening is a perversion on what religion is actually supposed to be. Several lines point to the "perversion" aspect ("twisted baptism of fire", as opposed to baptism by water, for instance). It's a dogma stripped of all of the virtue that's supposed to be its source. This doesn't seem to me like a condemnation of all religion--just human misuses and human creations passed off as religion. VERY fascinating one from a lyrical perspective.