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Setup a port knock daemon which opens the firewall for some time when specific ports are "touched" in some specific order. See for more information Port knocking
You start by figuring out what's going wrong with your logging. Everyone on the Internet has an IP address -- it's a necessary condition for connecting to any other computer out there.
@david is correct that an attacker must be privileged: this is a MITM attack. There's another important detail: both users (server and client) must be using a vulnerable version of OpenSSL. For the web, while many servers use OpenSSL, none of the most popular clients do. None of Chrome, IE, Safari, Firefox, or Opera on the desktop use OpenSSL. See Which ...
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