Possible spoilers.
To use a level four limit on someone, you have to learn all the other limits they can learn (other than Vincent and Cait Sith all characters have two level one limits, two level two limits, two level three limits and one level four limit).
Locations:
Cloud, Omnislash: Gold Saucer, Battle arena, can be brought for 32,000 on disks two and three, approx 50,000 on disk one.
Barret, Catastrophe: talk to the woman in the hut after you get the Huge Materia and save the town there.
Tiffa, Final Heaven: Nibelheim (Cloud and Tiffa's home town) With Tiffa in the party on disk two (after you get Cloud back), play the song Cloud played on the piano in the flashback in the Kalm inn, I'm not sure what the notes where but I think they where Do, Re Me, So, Fa, La, Ti, Re, Me, Do.
Aerith/ Aeris, Great Gospel: Once you have the Tiny Brocco, go back and get in to the Buggy, go into Costa De Soul while in the Buggy and take a boat back to Junnon, From Junnon follow the river until you find a shallow part that you can cross, on the other side you will find a cave with a man inside who will tell you how many battles you've been in (if he sais something else exit the cave and re-enter), the last two digits have to be the same eg. 211, 222, 233, 244 he will give you Mythril, go back to the desert under the Gold Saucer, look across the river and you should see a house, go in side the house, give the man the Mythril and choose the Small box which will have the Great Gospel inside (The Big box has a Gold bangle).
Red XIII, Cosmo memory: Nibelheim (Cloud and Tiffa's home town), in the Shinra mansion, unlock the safe in the room on the second floor and beat Lost Number, the combination is: Right 36, Left 10, Right 54*, Right 97.
Yuffie, All Creation: Beat Yuffie's side quest in Wutai and then beat the 5 story building.
Vincent, Chaos: Behind the waterfall between the Gold Saucer and Nibelheim (you need Vincent with you).
Note 1: You will need a Green chocobo or the Sub to get there.
Note 2: After you go there the first time you will have to go there again after about an hour to get it.
Cid, Highwind: In the sunken plane, you will have to dive in the sub close to the Gold Saucer.
Cait Sith doesn't have one.