"log on to" and "log in to" are both used. I personally prefer "log on" when the object is a computer (as opposed to, say, a service). "log onto" and "log into" are substandard in my opinion. Similarly, I prefer "dial(l)ed in to" to "dial(l)ed into".
"computer login" and "computer log-in" are both used, though I prefer the latter. Same for "login/log-in password".