Bring small pot of water to a boil. Add eggs and cook for 10 minutes. Remove from stovetop and place under cold water to stop cooking and begin to cool eggs.
While eggs are cooking, chop the potatoes into roughly 1/2"-3/4" cubes, depending on your preference (and mouth size)
Add potatoes to stock pot and cover with cold water. Place on stove and bring to boil over high heat. Cook potatoes until they can be easily pierced with a fork. Probably around 10 minutes, depending on size of potato pieces. The safest bet is to check them periodically with the fork. FORK IT!
Once the potatoes are easily pierced when forking them, remove from boiling water into a colander and rinse with cold running water to stop the cooking process and cool the potatoes slightly. This will prevent the potatoes from overcooking, due to the residual heat inside the potato pile.
In the meantime, begin chopping your celery, pickles, red and green onions.
Peel and chop the hard boiled eggs into eight pieces each. (cut length wise, then cross wise, and then cut each of the four pieces into two pieces, for a total of eight). Repeat for each egg.
Place the cooked potatoes into a large mixing bowl. Add all remaining ingredients and stir gently until just combined.