Rapture
 
Rapture Stage Fashion Rapture Swimsuit
First appears in The Stingers Hit Town Part 1 and again in: 

The Stingers Hit Town Part 2, The Day the Music Died, That Old Houdini Magic, Straight From the Heart, Riot's Hope, Change of Heart, A Father Should Be....
First appears in The Stingers Hit Town Part 1 and again in: 

The Stingers Hit Town Part 2, Change of Heart. 
Rapture Egyptian Servant Rapture Wicked Witch
Makes it's first and only appearance in The Stingers Hit Town Part 1. Makes it's first and only appearance in The Stingers Hit Town Part 2.
Rapture Masseuse Dr. Rapture
Makes it's first and only appearance in The Stingers Hit Town Part 2. Makes it's first and only appearance in The Stingers Hit Town Part 2.
Rapture Tiger Striped Pants fashion Rapture striped tube top fashion
First appears in The Stingers Hit Town Part 2 and again in: 

Midsummer Night's Madness, The Day the Music Died, That Old Houdini Magic, Change of Heart. 
First appears in The Stingers Hit Town Part 2 and again in: 

The Day the Music Died, Straight From the Heart.
Rapture Festival of Mythology Costume Rapture Oracle of Athens
Makes it's first and only appearance in Midsummer Night's Madness.

The bottom of the tights and shoes are a guess (they are what is seen under the Oracle cloak).

 Makes it's first and only appearance in Midsummer Night's Madness.
Hat/jewellery Straight Jacket w/pink ribbons
Makes it's first and only appearance in That Old Houdini Magic. Makes it's first and only appearance in That Old Houdini Magic.
Rapture Tux and tails Outfit Rapture Houdini cape fashion
Makes it's first and only appearance in That Old Houdini Magic.
Makes it's first and only appearance in That Old Houdini Magic.
Rapture Wingwalker Rapture Royal Flash
Makes it's first and only appearance in  Straight From the Heart.
Makes it's first and only appearance in  Straight From the Heart.
Rapture Blue Cape Busking Rapture
First appears in Straight From the Heart and again in: 

Change of Heart. 
Makes it's first and only appearance in Riot's Hope.
Orange Stage Fashion Rapture
Makes it's first and only appearance in Riot's Hope.