I can narrow some down off the top of my head:
Biomech - Waist
Believe this is a 1/3 chance item from the Flash's in the Old Star Labs instance.
Barbarian - Head , Waist , Feet
Barbarian items drop extremely rarely as green 30 items, and are more common on the hero side's auction. Otherwise, hope for good vault luck. I'm still missing Head/Waist myself.
Egyptian - Back , Feet
I think the Egyptian back is off a rare item from Isis, solo mode, 1/4 chance. The feet, I don't recall although I have obtained the style, perhaps from the vault. Personally I'm missing the shoulders.
Insectoid - Chest , Back
Both are from Bludhaven. Chest is a no-drop blue from Chemo, back is a no-drop blue from Bludhaven avenger. There may be other items with this style (Hive Moon Base or some other alert?), but I know those are the most common places to see them.
Kabuki - Head , Legs
Kabuki pieces are all from duo boss drops, and unfortunately are a bit rare, perhaps 1/5 chance to drop. Legs should be from OMAC servitor (the guy after the turret ring event with the orb-shield and the drone phase in the middle). Head is off Mr. Freeze.
New Genesis - Feet
I obtained this style via the vault. I'm not sure how else to obtain it.
Contemporary Tech - Back
This style drops from the Green Lanterns outside of Metro City Hall or from Gotham police where you have to do lure cops by rigging the cars. Both enemies are level 19-21. The item is droppable but I never see it for sale on the AH and spent about an hour slaughtering Green Lanterns for it. The item is called a "-------- Synthium Backplate"
Military Tech Chest, Back
Duo-mode Bane drops the Chest, duo-mode Isis drops the back.
Retro Tech - Shoulders
Still looking for this one myself. Vault might be the best chance?
4th World - Head , Shoulders
Both Head and Shoulders are from blue(rare) droppable loot from chests in HMA's, they also drop in the vault. Head is extremely rare for most everyone.
Tech Ninja - Shoulders, Waist, Legs
All of the tech ninja styles are available from blue(rare) loot from chests in HMA's. Since they are all droppable, they sometimes appear on the Auction, although for twink-character prices of 10k-30k. I believe there are alternative items for this style that drop from places such as from OMAC base or from Gorilla Island lower level alert, but I do not know if they include shoulders, waist, and legs.