Nonconformist

You have to be a confomist and act like a Goth if you want their help. Hypocrites.

Summary
Get coffee, cigarettes, and goth clothes to make the Goths join your fight.

Walkthrough
First, go over to Tweek Bros. Coffee and buy a Dark Roast from Mr. Tweak. On your way out, you get jumped by several elves. They'll give you the option to either come with them without a fight or to battle them.

Note: As the elf says, it's completely pointless to fight them, as you'll gain no experience from the battle and one of the elves will hit you with his hammer and knock you unconcious afterwards.

Either way, you're taken to the Elven Kingdom afterwards. Kyle tells you to join them against Cartman, because he secretly is hiding the stick. Stan will follow you now. Go to Jimbo's Guns. There will be sixth graders smoking in the alley. Defeat them, and they'll drop cigarettes.

Finally, go to the U-Store It next to Tweek Bros. and buy goth clothes from the hobo. Return to the Goths, who have one final request. Take a picture during the PTA meeting holding a "Fuck the Conformists" sign. Head to the community center next to the school. This quest is continued in PTA Problems.