The crew are arguing over whether to buy Talika or not
D: Pay them
R: But...
J: Sparky, cough it up
Cough it up is a slang expression meaning to give something up or relinquish it. It is most often used when someone is reluctant to do so.

Talika comes across John whistling and swinging a slinky around
J: Hey, hey, how ya doin'? come on in. Sorry about the mess. Chocolate? Fresh from Earth.
John certainly made use of his time on Earth to stock up on things he's missed, particularly chocolate. Additionally, John is whistling a bit of classical music, the name of which I can't place at the moment (I need to go through my cds since the whole tune is now stuck in my head), and he is playing with a Slinky. New! Thanks to a site fan who identified the piece of music John is whistling as "Eine kleine Nachtmusik" by Wolfgang Amadeus Mozart.

John tries to separate the feuding D'Argo and Rygel
J: Break, break, neutral corners.
A reference to wrestling or boxing, though I tend to lean toward wrestling since John has demonstrated his appreciation for wrestling in the past.

John finds out Rygel has cheated the traders
J: Ryg, you can't do stuff like that, you're jamming us up.
D'Argo and Rygel go at it again
J: Chill, chill
John has slipped completely into his Southern/Surfer personae. Anytime he's feeling groovy or he's under mind control, his Southern accent becomes more pronounced, and he acts like the most chilled out, easy going, Surfer dude.

J: Pilot, can you get that trading ship on the phone?
P: I'll try, Commander, but this area of Tormented Space is making transmissions very unreliable.
J: You can do it, Man. You're smart enough, you're good enough, and doggone it, people like you!
P: Are you all right, Crichton?
Of course he's all right! He's just helping Pilot out with his Daily Affirmation. John is actually quoting from a Saturday Night Live skit called "Daily Affirmations with Stuart Smalley" created by Al Franken. Stuart was a self-help guru who would end each "show" admonishing all viewers to repeat after him, "I'm good enough, I'm smart enough and doggone it, people like me."

John has been jumped by an oversexed Chiana
J: Man, she's in overdrive today.
Overdrive is an automotive term, it is a gearing mechanism of a motor vehicle engine that reduces the power output required to maintain driving speed in a specific range by lowering the gear ratio. (definition courtesy of Dictionary.com). It is also slang to mean a hightened state of activity or concentration.

J (to Scorpius): You think Talika's doing a T'raltixx, a mind frell? Let's go talk to her.
John is referring to episode 3x04, Crackers Don't Matter. Also, "mind frell" is a riff on "mind f***" which is used to describe someone's efforts to drive you crazy.

John and Aeryn are looking for Talika
J: Come out, come out, wherever you are.
Double reference here. First, to the children's game of hide and seek. Secondly, it is a reference to (surprise!) The Wizard of Oz. When Dorothy arrives in Munchkin land, Glinda appears and calls to the hiding Munchkins, "Come out, come out, wherever you are and meet the young lady who fell from a star."

Noranti and John work out a plan to find the energy orbs Talika has hidden
J: So we wake [Scorpius] up, use him as bait, and let her harvest his mojo.
I was expecting a mojo reference when Chiana announced her sex drive had been stolen. It came a bit late, but it's here. In the movie, Austin Powers: The Spy Who Shagged Me, Dr. Evil goes back in time and steals Austin's mojo, rendering him "shagless" and ineffective against Dr. Evil.

J(to Talika): I was planning on grabbing those 'nads there, but I guess you won't let me.
John is referring to the neural energy orbs. 'Nads is short for gonads. I think we covered this one in a previous episode. I leave it to the viewer to make the connection.

John manages to destroy the Talika spider monster
J: Along came a spider, exploded beside her.
Ah, fractured fairy tales, or nursery rhymes actually. The original quote is "Along came a spider, and sat down beside her." from the nursery rhyme "Little Miss Muffet."

J(to Aeryn): You're the key, my Achilles
"My Achilles" is a reference to the term "Achilles Heel." An "Achilles Heel" is a person's only or at least his most vulnerable weak spot. The term comes from the Greek myth of Achilles whose mother so feared her son's death that she took him and dipped him in the River Styx thus rendering him invulnerable. However, she held him by one heel as she did this, thus leaving him with one vulnerability. During the Trojan War, he was shot in the heel and killed.