They all work. Different places use different terms. Just don't mix/match... ie no Sign In / Logout. Sign In/Sign out is slightly less "computery" but everyone knows what all the variations do. Use the one you like best.
The second reply (The test is broken!) made me smile.
This is a pet peeve of mine as well. Similarly, "backup" is a noun, "back up" is a verb, but they're often abused.
I prefer to s/backup/archive/, since the word "archive" has the advantage of being both a noun and a verb.
Do you also hyphenate email?
Why not? English has been nouning verbs and verbing nouns for centuries. Grammar Nazis, logout! :-)