Jonathan Coulton/WMG

Code Monkey is the prequel to either The Future Soon or Skullcrusher Mountain
Specifically, the line "Code Monkey just waiting, for now/Code Monkey say someday, somehow" seems to suggest a Who's Laughing Now? sometime in the future where the Code Monkey becomes a Woobie, Destroyer of Worlds akin to Dr. Horrible (though much more successful). The girl in Skullcrusher Mountain could possibly be the girl at the front desk who rejected him or Laura from The Future Soon.

"Skullcrusher Mountain" is the sequel to "The Future Soon."
"Skullcrusher" comes right after "Future Soon" on the album, and the two songs sort of blend together. And the kid in "Future Soon" is fantasizing about forcing the girl who rejected him to be his wife after his robot army destroyed the earth and she lost her eyes in the resulting war. I really don't have a hard time believing that a little kid who dreams about that would roll a natural one on his "Understanding Love" check some years down the road.

The singer in "Skullcrusher Mountain" and "The Future Soon" is Dr. Horrible/Billy.
With "The Future Soon" coming before the sing along blog and "Skullcrusher Mountain" coming after. It makes a strange sort of since, both Dr. Horrible and the protagonist(s) in the song are predisposed to amazingly catchy musical numbers and super-villainy AND both have humorous yet tragic romantic lives.

Better is the sequel to The Future Soon, being sung by Laura
The protagonist of The Future Soon eventually won Laura's heart, but insisted on replacing "the things that make him weak and strange" anyway. Laura had grown to like him fine originally, before he "looked like the victim of a surgical crime".

"The Future Soon" is a major turning point in the Jocoverse's timeline.
Notice how many of Coulton's songs can be put into a universe that basically reflects the real world or a fantasy/sci-fi world. Basically, based on the choices of the protagonist of "The Future Soon" alter the course of the future, two different timelines described in various songs.

The "realism" timeline happens when the kid forgets his fantasies, matures a little and grows up into the protagonist of "Code Monkey." He's long since gotten over Laura, but his social skills are still lacking, and being rejected by the receptionist results in him becoming more and more depressed. He goes to a psychiatrist and eventually ends up on antidepressants, leading to the events of "I Feel Fantastic." In time, he makes a little more progress, gets married and reaches middle age, but is not entirely satisfied with his life, even when he moves out to the suburbs in an attempt to start over. Welcome to "Shop Vac."

In the "sci-fi" timeline, he begins to focus more and more on science, but unfortunately his sanity deteriorates, not noticeably at first... his advances in science sufficiently impress Laura, who he ends up in a relationship with, but he attempts to upgrade her like he initially envisioned doing to himself. This causes her to essentially lose all humanity, which causes his mind to break altogether and he projects his guilt and blames her instead ("Better"- he outright says he blames her, and note how the first thing he mentions is "infrared eyes" like the "bionic eyes" of "The Future Soon"!). He snaps and goes full-out supervillain ("Skullcrusher Mountain"), sending out Scarface in attempts to find a replacement for Laura. He scraps the cyborg plan altogether and, after some thought, decides against igniting the atmosphere in favor of having robots infiltrate society as hired help, first completely harmless then introducing deadlier robots as "upgrades" ("Todd the T1000"). Of course, as we all know, A.I. Is a Crapshoot and the robots rebel and take over, leading to humanity being enslaved by robot overlords ("Chiron Beta Prime").

You could probably connect every song like this, but that's all I've got for now.

The protagonist of "The Future Soon" is in a wheelchair and/or has some other disability
Hence why he wants to upgrade himself so he won't always be "weak and strange"- the other kids ostracize him for his disability because Kids Are Mean.

The eponymous Creepy Doll of Creepy Doll is a magic-enlivened serial killer.
It hasn't always always followed you, it's only followed you since you moved into the house where no one lives. It has done so for every tenant, using its powers to plant more and more creepy clues around the house and the town to mess with its victims' minds, and if the vicim either shows signs of having become used to the doll or becoming agressive (both of which you exhibit), it either ups the horror drastically or turns your attack back on you.

The main character from Creepy Doll is actually a criminal
This is why you moves to a house where no one lives in the woods. Also why you have multiple bags of big money, the one that you use to but your house and the one that's. You are a criminal trying to run away to the middle of nowhere. Also, the doll most likely his consciousness manifesting itself in his growing subconscious, eventually culminating in.