I don't know if there is a test for salt in soil. But there is something you can try. This is used with great success on coastal golf courses, where salt spray or salt water intrusion can create serious problems with the turf. I also used it in a container nursery I had some time ago, when salt water intruded into the well water.

Gypsum, when applied to the soil surface and watered in thoroughly, latches onto the sodium ions and prevents them from being taken up by the plant. The sodium is then leached out of harms way. Gypsum can be applied several times a year, and will not alter the pH of your soil. I would try to find the granulated or pelletized product, as the powdered gypsum can be a mess to handle.

Salt is absolutely tested in a soil test. Sodium needs to be in balance with calcium, potassium, and magnesium. If you get an over abundance of any one of these four elements, you will have trouble. But you can rebalance the imbalance by adding what you need to of the other three.

The best soil test lab in the world, that I know of, happens to be here in Texas. The Texas Plant and Soil Lab tests soils from around the world, so don't let the location put you off. They work with farmers all over to improve their yields and reduce disease. Because of their work we now have pecans that bear nuts every year (instead of every other year) and watermelons that fruit all year long.