Does in magento 2 exists event similar to event sales_order_invoice_save_after from magento 1?
Or, where should plugin "listen", to get similar functionality?
Yes, this event still exists. Just for your knowledge, I would like to share that it will always be fired whenever you made any change in order related data after invoice creation.
So it would be better to use "sales_order_invoice_pay" in case you want event to be fired only when first time invoice is created.
Check this link for list of all events and observer of Magento-2. I hope this will help you.