Heat grill to medium-high. With a fork, prick the sausages in several places. Grill, turning occasionally, until cooked through, 10 to 12 minutes.
Meanwhile, brush the tomatoes and onion with 1 tablespoon of the oil and season with ½ teaspoon salt and ¼ teaspoon pepper.
Grill vegetables until tender, 5 to 6 minutes per side for the onion and 2 to 3 minutes per side for the tomatoes. Transfer to a bowl as they are done.
Add the spinach to the bowl and toss.
In a small bowl, whisk together the vinegar, mustard, remaining 3 tablespoons oil, ½ teaspoon salt, and ¼ teaspoon pepper.
Slice the sausages and serve with the vegetables and dressing.