Halo 3: ODST
As a speedgame, Halo 3: ODST is not as popular as the others in the series. Levels tend to be linear and there is a lot of walking between levels.
In ODST full game speedruns, you start on Prepare To Drop, and you may use a profile that has the audio logs unlocked.
ODST uses the same engine as Halo 3, so Halo 3 tricks should be equally possible in ODST. However, tricks which rely on equipment are not possible, as enemies either do not drop equipment, or it is impossible for the player to pick up equipment in ODST.
Halo Runs record page: http://www.haloruns.com/records?lb=400 (click the timestamps for video links)
Unlocking 8 audio logs in Mombasa Streets will allow you to use Mongooses. See this link for the locations of all audio logs in Mombasa Streets. Some will not be able to be unlocked until you progress through the game. Audio logs ready to be collected will glow yellow in the VISR.