From Halopedia, the Halo wiki
The objective is to locate the skull(s) on the map and to maintain possession of it for the longest period of time possible. The default settings allow the game to be a free for all with one skull on the map, which players need to have possession of for two minutes in order to win. This game can be played as a Rumble Game or a Team Game where the highest score of the lone player (Free-For-All), or on a team's accumulative score, chooses the victor(s). Normally, a player who has the Oddball is the immediate target for the other players, which is what makes Oddball an extremely fast-paced gametype.
While a player has possession of the Oddball, they cannot wield their weapons or throw grenades. However, they can still melee opponents with the skull, which normally inflicts massive damage. In Halo 3, Halo Reach and Halo 4 multiplayer, if a player melee an enemy with the Oddball, it is an instant kill, but this can be tweaked via the game setting. The settings for the game can also be altered to make it more interesting. For example, the player with the Oddball can go invisible or can be slowed down. The number of Oddballs on the map can also be changed.
The Oddball's appearance is nearly identical through the original trilogy; the ball is a plain human skull. They are also identical to the skulls found in campaign in Halo 2 and Halo 3. In Halo: Reach the Oddball is on fire much like the Headhunter skulls. If the skull is dropped in water the flames are extinguished, though it will relight when it is picked up again. In Halo 4, the Oddball is a spherical container containing a light blue holographic skull. The "ball" part consists of black metal brackets that surround the skull. The brackets are positioned to emerge from the back of the skull and leave the 'face" area open. It also serves as the Grifball.
Halo 4 features the first noticeable gameplay changes since Oddball's inception in Halo: Combat Evolved. Players can now throw the Oddball using the grenade throw button (left trigger in default controls). Catching or intercepting a thrown skull awards medals. The skulls are also more noticeably affected by physics, bouncing off the surfaces and getting knocked around by explosions and Gravity Hammer strikes. Additionally, plays can perform Ballsassination — assassinations the skull — which vaporize the target like Forerunner weaponry.
Halo: Combat Evolved
Halo 2: Anniversary
Halo 5: Guardians
The following achievements can be unlocked in Oddball gametypes.