That looks like an outlet extender to me, plugged into a regular dual receptacle behind it. E.g. https://smile.amazon.com/GE-54947-Grounded-Adapter-Outlets/dp/B00006IBFA

Thanks for the reply - I will test this once I'm back home. All of the lamps are either plugged into outlets that have an adapter similar to this or an outlet that can be controlled by a wall switch. Not sure if this has an effect or not.

You could use something like this outlet tap and it should be safe to connect power strips to it as long as you are not exceeding the power ratings. But I do not know much so do your own research.