Who to call about sinking porch and mud room?
Foundation problems are NEVER cheap to solve, and sadly, someone got cheap when the work was first done. Do the work right the first time. Was this addition even inspected by the local building inspector? If not, then you may have some legal recourse if the owners did work and failed to get the necessary permits. I doubt it would work, but only a lawyer would know.

This is not your fault of course, except for buying the house in the first place. A good home inspector should have pointed this out and warned you of the cost to repair it at the time. It is yet another reason to have a home inspection done.

Given all of that, you are now stuck with a problem, that MUST be resolved. I don't even know positively that mudjacking can solve this, only a good mudjacking contractor will know for sure. No matter what, there will surely be some excavation involved, even if only to determine how much must be done to repair the problem.

Start asking around. There are foundation services companies around who specialize in problems like this. Get and check references. Don't just jump at the cheapest estimate you get.