The Other World is where you go when you die in Dragon Ball Z. The dead character first gets judged by King Yemma whether he goes to Heaven or Hell. The Other World is where all the highest deities reside. The 3 stages are Hell, Heaven, and there is a Stage between those two stages.
HellHell is where the people who have dealt great evil in their lifetime go in the Afterlife. It is also where Cell and Frieza now spend their days. Hell is held by Ogres who report to King Yemma. Once the villains took over Hell. But was stopped by Goku. In Fusion Reborn Goku, Vegeta, and Pikkon travel to Hell to fight Janemba. In GT goku fights Frieza and Cell here.
HeavenHeaven is where King Yemma sends people who have dealt good in their life time. It is where Piccolo went before he forced King Yemma to send him to Hell in the Super 17 Saga. It is seen as a planet that has a strange glow to it. It is filled with flowers and such.
The Middle Stage is never given a name throughout all the Dragon Ball series. It is where all the deities of the entire universe reside. Goku, Pikkon, and Olibu also live there. It is where people who keep there bodies go.