Preheat oven to 400 degrees F. Line 1 large or 2 medium baking sheets with parchment paper.
Prepare carrots by cutting them into small pieces and then drizzling them with some olive oil. Put them on the sheet pan and put them into the oven for 20 minutes, stirring halfway through.
While the carrots are roasting, prepare the other vegetables and sausage. Cut sausages into 1-inch slices and cut up the other vegetables.
In a small bowl, whisk together the olive oil, vinegar, garlic powder, onion powder, paprika, salt, and pepper. Remove carrots from the oven and add sausages and vegetables to the pan. Spoon/drizzle olive oil/balsamic vinegar seasoning mixture over the sausage pieces and vegetables on the pan, and gently toss to coat. Season with more salt and pepper if needed. Spread into an even layer.
Roast in preheated 400 degrees F oven for 30-45 minutes, turning everything about halfway through the cooking time. Test vegetables to see if they are done. Squash should be fork tender. The carrots tend to take longer to cook than the other vegetables.
Notes
This serves 6 to 8 people depending on the serving size.