Status codes 204, 304, and 1xx don't allow bodies. We already
had a function for this, but we were hard-coding just 304
(StatusNotModified) in a few places.  Use the function
instead, and flesh out tests for all codes.

Fixes #6685

R=golang-codereviews, r
CC=golang-codereviews
https://golang.org/cl/53290044