You do not need these to enter the Den of Woe, but they give more details on the lives of Nooj, Paine, Gippal, and Baralai.

Nooj's Sphere:
Chapter 5, Mushroom Rock. Note: This only happens if you gave the "Stolen Sphere" to the Youth League. Speak to Yaibal and accept the task to help Youth League members blow off some steam. Afterwards, go back to Mushroom Rock and proceed to Youth League headquarters. You can now go inside the headquarters. Lucil is on a balcony around the back. Speak to her and she will give you Noojie Woojie's sphere.

Baralai's Sphere:
Chapter 5: Guadosalam. After the "Episode Complete", return to Guadosalam. Find Trommell beside the door that has been locked throughout the entire game. Look for the treasure chest to get Baralai's sphere. Go back to the Celsius and ask Shinra if you can view it.

Gippal's Sphere:
This sphere is difficult to obtain. You must make Rin the culprit in The Mi'ihen Mystery (Chapters 4/5). He will give you Gippal's sphere in Chapter 5.

Paine's Sphere:
Chapter 5: In the Farplane. After you have made your way through the holes and played the organs and before you fight Vegnagun, you will reunite with Gippal. He hands Paine the sphere she left in her recorder. You get the chance to watch it then, and do not have to go back to the Celsius.