1986 Audi 5000 Hesitation under load

A 22 year old car with 200K on the clock can have certain issues that might be considered. First, There are components that can and do wear out, for example, the air flow meter uses a carbon film resistor to tell the DME how much air is going into the engine. Over time there can be a significant degradation of this carbon film. The performance (or lack there of) of any Bosch injected vehicle can and does depend on the information the Digital Motor Electronics receives from its sensors. If the data is compromised in some manner, then it is possible to "see" what the issue is and take steps to correct it. These steps might unfortunately carry a cost that exceeds the value of the vehicle (not to denigrate your car, but it is something to consider) I don't consider myself to be an expert on 1986 Audi 5000 vehicles, but I am knowledgeable about Bosch engine management and when I have a high mileage older car under my care with problems like you are experiencing, one of the first things I do is to create a relatedness with the customer and find out as much as I can about where the car has been, its history if you will, and try to eliminate what isn't wrong, and focus on a strategy that will hopefully avoid wasting time and money. Throwing parts at the car is not my favorite way of being, but there are components (such as the air flow meter) that should be replaced after the service life is reached. Also the electronics in the car have a component that is sometimes overlooked, the engine wiring harness. Intermittent issues can often be due to a poor connection within the harness and can be very difficult to uncover. My greatest desire would be to offer a "magic bullet" and say this is it right here, but I can't do that. Food for thought my friend, good luck and I hope you "get `er done"

well i just put a full tank of gas in the car and the problem was ALMOST non existent.. less hesitation and more power like it was. car sat for about 6 months and the problem was going on before that, but previously i accidentally ran it out of gas and on another venture i had an issue with boost spike and hit fuel cut at 18psi. it has an upgraded ECU among other things. Could this narrow down the problem and maybe offer up some more suggestions about what to do? what kind of harm could running out of gas or hitting the fuel cut have done and what would need to be looked at first?
Thanks for any responses...

Running the car out of fuel can damage the fuel pump. Fuel is what cools the pump. At 200K miles and with this information I would try replacing the pump and filter as a preventive measure and to possibly eliminate the fuel supply as an issue.