shawls, stoles, capes, serapes and ponchos are or can be worn over the shoulders. Shawls can also be worn over the head and shoulders.
The garment worn over the shoulders is spelt shawl.
A stole.
Cape has a few meanings - A sleeveless outer garment fastened at the throat and worn hanging over the shoulders. - A brightly colored cloth used in maneuvering the bull in a bullfight, or a point or head of land projecting into a body of water.
A bertha is a wide collar that is worn as a decorative garment around the shoulders and over the neck. It was a popular fashion accessory during the Victorian era.
I think you are talking about the stole (long rectangular scarf)
The outermost garment worn by a priest while saying Mass is called a chasuble.
A union suit is a one piece garment, which goes from the shoulders to the ankles. They are usually worn as pajamas or under clothing for warmth.
The brightly colored shawl commonly worn in Latin America is known as a "rebozo." It is a traditional garment that is draped over the shoulders and can be used for various purposes such as keeping warm, carrying goods, or as a fashion accessory.
stomacher
A Haik is a traditional Algerian garment worn by men. It is a loose-fitting robe-like garment that is usually ankle-length and worn over other clothing.
A cape.
Stomacher