There isn't an automatic way to do that today, but that feature would be very cool.
You may be able to do this by hand by adding a callback argument to your OpenID RPs and to your OAuth clients, such that it would appear in the URLs on both sides. But that wouldn't cause it to add the identifier to every single log message, which it sounds like you're asking for, and would be the ultimate feature.
I think this deserves some brainstorming on how we could achieve it.
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Andrew Arnott
"I [may] not agree with what you have to say, but I'll defend to the death your right to say it." - S. G. Tallentyre