The blue black wasps have moved in. I sprayed them with wasp-n-hornet spray. Will this eradicate them?

Just for a bit of info, wasps are pretty awesome. They kill and eat a lot of pesky pests in the yard such as tomato horn worms, and they also pollinate. There are many wasps that aren't aggressive and will mind their own business - people aren't food or a threat unless provoked. I have a couple of mud dauber nests near my front door, but mud daubers build their nests and leave within a few days. I've never encountered hornets, but I think they might be one I wouldn't tolerate near an entrance to my home. The wasp and hornet sprays will generally kill everything, including you if given the correct dose, so to answer your question, yes.

.  Those may be mud daubers. In which case, there is no need to eradicate them. Knock down their mud nests a few times and they will move elsewhere.

If you sprayed the nest, it should. It may take a little while.