Few of these should have lasted 18 years unless dumped on the soil at that location in extremely high concentrations. It is possible to have the soil tested, but you need to name the chemical for which the laboratory will be testing, and it is expensive. An experiment you might wish to try is to dig soil from the surface, six inches down, and a foot down. Place the soil in a flower pot, perhaps adding some sand to allow better drainage if the soil has a lot of clay. Then plant beans, or another broadleafed plant, and corn, or another grass plant.
Some herbicides are selective, killing only broadleafed plants or grass plants.
Others, and the micronutrient factors mentioned above, will affect all plants. By doing this you can determine the depth of the problem in the soil, if it is selective, or if the problem is really in the soil. After you have done this, contact your local Cooperative Extension Service Agent again with the results of the experiment, with soil nutrient test information, and information about irrigation. Perhaps then the solution will be apparent, even if it involves removing the top six inches of soil in the area or diluting it with soil from another area.