What is the largest aircraft that has been flown inverted successfully?
Theoretically ANY airplane can be flown inverted, if you know what you are doing with it and make sure it is loaded properly throughout the maneuver.  Boeing test pilot Tex Johnson famously rolled the 707 prototype - twice - during a demo flight for airline executives at the SeaFair hydroplane races on Lake Washington in Seattle.  He nearly got fired for the stunt but the plane was perfectly fine.


                
            

The real issue is load factor: the total load imposed upon the wings divided by the gross weight of the aircraft.  Don't exceed theses values and have the aircraft flown within the required speed range and it doesn't care whether it's erect or inverted during the process.

In general though, unless an aircraft is specifically designed for inverted flight with inverted i.e. negative G fuel and oil systems, inverted flight must be maintained with a positive load factor to prevent fuel starvation and damage to the engines.

As a side note to this, DO NOT TRY AEROBATICS IF YOU HAVE NO FORMAL AEROBATIC TRAINING AND/OR ARE ATTEMPTING TO DO SO IN AN AIRPLANE IN WHICH THEY ARE NOT APPROVED.  It's true guys like Sean Tucker have done aerobatics in a Cessna Corvalis but those are experienced airshow demonstration pilots with over 20,000 hours of logged flight time and more experience at the edge of the envelope than you can shake a stick at.  You do not have this prerequisite experience and most likely will kill yourself attempting these maneuvers.