Most likely, the Black Walnut tree roots are affecting the tomatoes and potatoes. Many sources say that tomatoes and potatoes will not do well planted within the dripline of a Black Walnut tree.  There is not a test available to determine if the Black Walnut roots are the cause of your wilting plants.  However, you can have your tomatoes tested for Fusarium and Verticillium wilt at the Plant & Pest Diagnostic Lab on campus: https://www.canr.msu.edu/pestid/

Next year, if you have the space, you may want to consider moving your vegetable garden well outside of the dripline of the Black Walnut tree.  

Something else to consider: Did you plant tomatoes and potatoes in the same spot last year?  If so, it's a good idea to rotate your crops each year.  Potato, tomato, all peppers, tomatillo, and eggplant are all in the same family, so you would to plant your tomatoes and potatoes in a different area.  Rotating your crops will decrease the chances of crops obtaining a disease that may be leftover in the soil from the year before. 

Here are a couple of articles that talk about planting tomatoes near a Black Walnut tree.  
https://ucanr.edu/blogs/blogcore/postdetail.cfm?postnum=15061

https://hnr.k-state.edu/extension/horticulture-resource-center/common-pest-problems/documents/Walnut%20Wilt.pdf

Your asparagus may or may not be affected by proximity of the Black Walnut tree.  Asparagus takes a couple of years to fully establish itself.  Here is a great article on growing asparagus: https://www.canr.msu.edu/resources/growing_asparagus_at_home

You may also want to consider a soil test for your asparagus.  A pH of 7 is ideal and a soil test will let you know the organic matter and nutrient content.