These are the same links as other parts of the site (probably), but are grouped by construction method.

There Are a number of ways to make  kazoo bodies (or anything else)
Fabrication--take a flat sheet of material, such as metal, paper, plastic, etc. and cut, fold and/or glue or solder etc to form a body.
These paper ones could be adapted for metal and other materials.
PAPER
 Paper Kazoo 01, Paper Kazoo 02 Round Bottom,  Paper Kazoo 03 Quarter Circle Cone,
  http://www.instructables.com/id/100-Kazooz-in-my-pocket/,
Paper Mirlitons
Images on Flickr of two mirlitons to make from paper or thin cardboard.
The instructions are in French, but it is not too hard to follow the pictures
http://www.flickr.com/photos/taffeta/3901667363/
http://www.flickr.com/photos/taffeta/3059359705/
http://www.flickr.com/photos/taffeta/3060194038/


Molding--take a mold and apply the substance you wish to make the kazoo out of, such as plastic, clay, paper strips, paper pulp, fiberglass, candy, etc. when firm enough the object is removed from the mold and possibly has other parts and/or finish applied to it.  In some cases the mold can be purchased, an existing object used as a mold, or a mold made from scratch.
Chocolate Kazoo
http://beccajones.blogspot.com/2011/07/kazoo-chronicles.html
http://beccajones.blogspot.com/2011/07/kazoo-success.html


Found Object-- Take existing object, such as a cardboard roll, cigar tube, candle stick, etc. and add a membrane.
Clothes Pin Kazoo
http://voiceofthemonkey.com/2011/07/27/kazoo-provided-by-combining-clothespin-and-strip-of-paper/

Cardboard Tubes
http://boowakwala.uptoten.com/kids/boowakwala-adventures-orchestra-kazooactivity.html
http://jas.familyfun.go.com/arts-and-crafts?page=CraftDisplay&craftid=10526
Foil Membrane Kazoo
http://www.ehow.com/how_12064436_make-kazoo-foil.html

Decorative Horns
Kazooed Horn


The above methods are additive.
Subtractive--(There may be a better name for this. I just can't think of it now.)Take a solid object, such as a piece of wood, metal, clay, etc. and remove parts to form the body.   This can include the use of a lathe.

Wooden Kazoos
 http://boyslife.org/hobbies-projects/projects/7346/how-to-make-a-kazoo/
http://www.youtube.com/watch?v=F0zNRO7xVDI

Carrot Kazoo
 http://www.newworld.co.nz/differentlikeyou/workshop/carrotkazoo


Bamboo Kazoos
HAGAMOS UN MIRLITON DE CARRIZO Navachiste 2009
YouTube Video showing making mirlitons from bamboo in South America.
http://www.youtube.com/watch?v=xO0H3Fz0ocU

Jamboree Freedom in Education 
Make a kazoo from an elder branch or bamboo
http://www.jamboree.freedom-in-education.co.uk/w%27s%20craft%20corner/kazoo.htm