Who should I hire to clean my Buderus boiler?

Have your oil company clean your boiler , they would be the best to work on a oil burner unless the plumber worked in the oil industry ..

Pictures of fouled up boilers with zero context. Personally? when I was doing oil service my goal was the make and keep our customers happy and their systems running as best as possible. I never or rarely ran into a service tech who didn't care. Maybe I ran in rarified circles.

In Cape May County there were two Full Service fuel dealers that employed their own service technician during my time doing oil burner service there.  There were about 6 other oil only dealers there. One of those full service companies had some techs that knew their stuff.  There was another that had someone that already "Knew it all" and did the majority of that company's oil burner repairs and the occasional boiler replacement.   When that one tech retired, that company got around to contacting me, as a self employed sub contractor, to fill the gap.  I found so many customers that had sooty boilers and furnaces that I could not believe that this company was able to keep their customers from switching to gas.   After 2 years of maintaining these boilers I was able to reduce the fuel usage significantly of many of the customers and management decided that I was not a team player and elected to hire someone in house to do the oil burner work. (long story involved here)

So it is hit or miss when hiring an oil burner service person. For the most part, if you have a family owned oil company (they are becoming rare)  that offers a full service company approach to keeping your oil burner operating dependability and efficiently, that is your best bet for the long run.   If there are several fuel oil only dealers (often called discount oil dealers) in your area and you happen to be using one of those for your fuel delivery, then there should be a self employed oil burner person, or an HVAC or Plumber that has a good oil burner tech that is available to all the customers that need service when their oil delivery company does not offer service and repair for those customers.    I happened to be that HVAC company from 1979 up to 2018.  I worked on customers that purchased fuel from 6 different fuel dealers and was careful to remain neutral when recommending one oil dealer over another.  If you owned an oil delivery company and you sent me your customer for repair or maintenance, I did my best to make sure that person stayed your oil customer. And the fuel dealers recommended me more often that way because they knew that I was not going to lose them any customers because of me or the techs that I employed.   

All that said, Once you find a company with a good burner technician, do your best to stay with that technician. (even if that tech changes jobs and is hired by someone else.)  In the oil burner service business, the technician that is the best often finds that doing the maintenance part of the job is beneath them. As a result you get the rookie that will be doing the maintenance portion of the work and only get the "good at what he does" technician after you have a problem that was not solved by the rookie. That's just the way it is in the trades. We all got to learn somewhere and sometimes that learning happens at the customers home.