Q:
Is there some way to tell what machine is claiming a license?
A:
You can do this, though it's not absolutely reliable.
After OmniWeb quits, type "netstat" in a Terminal window. Look for tcp port pairs that have the port 2453 on each connection, and with a host you do not recognize. That is the most likely candidate on which OmniWeb is being run.
This will work if no one is using -NXHost and Distributed Object apps across the net.