Peel and cut the potatoes into 1-inch dice and cook them in a large pot of salted boiling water until tender but still a bit firm. Drain, rinse with cold water, and place them in a large salad bowl.
Boil the eggs for 10-12 minutes, peel, and chop.
Make the dressing: combine the mayo, Dijon mustard, vinegar, paprika, garlic powder, freshly ground black pepper, and celery salt, until smooth. Taste it and add salt if needed.
Pour the dressing over the potatoes. Add the chopped onion, chopped eggs, celery, sweet pickle relish, salt, and pepper to taste. Toss gently until well combined.
Cover with plastic wrap and refrigerate at least 30 minutes prior to serving.