Heat the olive oil in a large pot over medium heat. Add the onions, carrots and celery. Cook for 5 minutes, stirring frequently.
Next, add the minced garlic and oregano, and cook 1 minute while stirring.
Stir in the diced tomatoes and the chicken broth, while gently scrapping any bits off the bottom of the pot. Raise the heat to high and bring the soup to a boil.
Once the broth is boiling, lower the heat to medium-low, cover and cook for 10 minutes. Keep the soup at a simmer.
Add the orzo to the soup, cover the pot and cook for 5 minutes (still on medium-low). Stir the soup occasionally to keep the orzo from sticking to the bottom.
Add the meatballs to the pot, cover and cook another 5 minutes, stirring occasionally.
Add the spinach to the pot and stir as you add it in. Continue cooking the soup for 2-3 minutes until the spinach is wilted.
Taste the soup and add salt if needed. As a reference we added ½ teaspoon to our soup.