Log in / out is more technical sounding than sign in / out. That said, I don't think there is any confusion with either one of them. The last time I looked at major sites using log v. sign it was a pretty even split between them. I would opt for sign in / out simply because it is more human speak.
Regarding Join, Register and Sign up. They each have slightly different meanings language wise, although even here I doubt that it will be critical.
For my (arguably subjective) take on their meanings:
- Join is when it's a club. You join a rowing club.
- Register is used when you are simply adding your details to some system for future use or access. You register to vote.
- Sign up usually has the connotation of a service or conference. You sign up for the military, or sign up for this conference.
The best thing that you can do is to ask a representative sample of your audience what is clearer and more human to them. Then go with that.
Edit: Something to consider is using "Sign up" and "Log in" as they are further apart visually and faster to scan than using "Sign up" and "Sign in".