What happens when there is conflict (priorities, dependencies, technical standards etc.) between 2 or more teams?
That's what a SoS meeting is for - not necessarily to resolve the conflicts, but to identify them and coordinate and facilitate the resolution.
How do the multiple teams maintain a co-ordinated direction when different team members may attend the SoS each time?
Typically it's the same person each time, usually the scrum master from each team. Sending the same person tends to work better as the SoS group learn how to work well together.
Is there an overall product owner?
Depends if there is an overarching product/portfolio. SoS can be used as a way of scaling agile, in which case there will often be a Portfolio Owner/Manager (who is responsible for multiple Products). But in other instances SoS is just used as a way to coordinate multiple loosely coupled products (and in that instance they may each have their own PO but no Portfolio Owner).