I have a calendar overlay of 7 calendars in SharePoint 2013. I'd like to synchronize a standard list with the overlaid calendars or a query all the calendars to update my list. Any ideas on how to do this?
You can attach a workflow to your calendars that updates your list or vice versa (enter on the master list and copy to other calendars). This is pretty easy to do, even if you have never created a workflow before.
SharePoint Designer Workflows: https://msdn.microsoft.com/en-us/library/office/jj554671.aspx
The next step up is trying to create a custom solution. you can use do this in SharePoint designer with the client side object model, or create a SharePoint hosted app to handle this. You would want to either hard code the references to the calendars or do a query to find them dynamically. Then you can load each one and iterate over the items and then copy them to your specified list.
Another consideration may be to not synchronize with another list but just leverage Search. You can create a search query to return all Calendar items from your designated sources. You can use a custom display template to render the results in a list type format.
Mathew McDermott has a pretty good get starting reference on his blog (and there are plenty of other examples on the web): http://www.ableblue.com/blog/archive/2013/06/05/introduction-to-sharepoint-2013-display-templates/