Well to answer your original question Awesomium is a webkit embeddable HTML rendering engine (of sorts). Not sure why or how ESO would be using it unless they are using it for chat or some of their UI.
Name's Raif, and I'm the Overwolf Community Manager.
Just wanted to weigh in and say that it is definitely not from Overwolf (not one of the processes we run).
For those who are having trouble with Overwolf and ESO, it's because we don't support it (yet!). We'll be releasing support for it soon. There was a change from something from beta to launch that we had to pull support for it last second but we will be releasing it soon.
Overwolf Community Manager - Here to help in any way