If you need an ironic slang term - I like this one: "super-low-end camera".

"Lowest-end camera" also emphasies how primitive it is.

"Point-and-shoot camera" is very popular and, while it sounds conversational, has become more or less the official term; it mostly means that it is very automated, but not necessarily fully compact.
( http://en.wikipedia.org/wiki/Point-and-shoot_camera )

You can also combine them and come up with something like
"lowest-end point-and-shoot camera".

Or, "cheap digicam", "cheap pocket camera".