It depends what you call the "corporation war", and I suppose the first Skaarj invasion refers to the Human-Skaarj war ?
Basically it goes like this :
-The Skaarj invade Na pali
-Vortex Rikers crash on Na pali and Prisoner 849 (the player) fight their way on the Skaarj troops to escape. In the process you kill a Skaarj Queen, igniting the attack of the Skaarj against humans. (Events of the first Unreal).
-The 7 days siege of earth, where the humans are able to destroy the mothership and repel the Skaarj. (Playable as an Assault map in UT2k4).
-After the end of the war against the Skaarj, the different corporations try to get advantage of the destruction to get hold of more territory on earth. The NEG indeed try to get some sort of control over the confusion. (Playable as an Assault map in UT2k4).
-The Strider war.
-Some strange artefacts are discovered and corporations fight to obtain them. (Unreal 2 events).
-To channel agressions, mining corporation start to legalize violence in small leagues.
-As the popularity of these leagues rise, the Liandri Corporation ,with the help of the NEG, start promoting and broadcasting bigger leagues with prizes.
-Malcom become the grand champion of the tournament, dethroning the previous holder of the title : Xan. (UT99 events).
-Another Tournament, where Gorge of the Juggernaut team finally get the title of champion, and snap Malcom's spine in the process. (UT2k3 events).
-One year later, the twelfth Tournament is hosted, with more team present and the return of Malcom. (UT2k4 events).
-War beetwen humans and Necris. (UT3 events).
-Izanagi corporation hires Malcom to run special ops One of the team he lead is nicknamed "Ronin" with the mercenaries known as James "Reaper" Hawkins, her sister Jester, Othello, and Bishop. The Ronin try to push further and get killed by the Necris when fighting on their homeworld. (UT3 events).
-The 523rd Nakthi Ascension Rites are starting. The Nakthi have to get a new Emperor via a series of combat. Anubis is one of the participant, and win the title. (UC2 events).
I only placed the "main" events, if possible in order of the timeline, but notice that I haven't put any consistent date, as they're unknown or often retconned it's actually hard to place things precisely. Also there's a lot going on in beetwen these events.