There are a few ways you might approach this. I've found that the simplest for us is to simply write the data to the task record, which is what we do with form submissions as well.
We created a custom integration event for webinar attendance. It creates a task (assigned to the Eloqua integration user) associated with the contact and writes data such as attendance time, questions asked etc. into the comments field of the task.
I can share more about the details if you want to go this route.
Another option would be to create a custom object in Salesforce to store the data, and create that instead of a task. In our setup we felt that would be more trouble than it was worth, but there might be good reasons for it such as not wanting to clutter up the activity list.