Cut kielbasa into 1/2" slices; set aside. Cook potatoes in a medium pan of boiling water until just barely tender, about 10 minutes; drain and set aside.
Heat oil in 4-5 quart pan over medium-high heat until hot. Add carrots, onion, celery, and garlic; cook stirring frequently for 5 minutes or until tender. Add mushrooms, tomatoes, tomato sauce, oregano and pepper. Bring to a boil; reduce heat to medium-low, cover and cook 20 minutes.
Stir in kielbasa and cooked potatoes; cook stirring occasionally for 15 minutes or until heated through. Add salt to taste.