I've usually heard people say only "forward" (never "forwards"), but I often hear both versions of the other two. Which are right? Are there rules that determine whether the s is added or not?
There's rarely, if ever, any need to try to write in anything other than your natural form of English. I have English, Canadian and U.S. publishers and never alter my spelling or style. I submit in British English, and let my editors do with my books as they will.If you're an American writer targeting American publishers, you're probably best using the 'sans-s' versions. Vice versa if you're a British writer targeting a British audience.
To confirm, the 's' versions are typical British English usage, while the 'sans-s' versions are typical American English usage.
There's rarely, if ever, any need to try to write in anything other than your natural form of English.