All commodity companies and prices soared at the same time, it wasn't at all isolated to Halliburton or oil. That was due to a debased dollar, which also sent all dollar-based GDP numbers skyrocketing around the world simultaneously. Go to Google and type in: "Czech GDP" or "Colombia GDP" (or dozens of other nations) and witness the incredible spike from ~2003 to ~2008, that's the dollar in action (ie the dollar losing value). Gold similarly soared historically for the same reason. It all crashed simultaneously as well. Those GDP figures almost all have gone down since ~2013, that's the dollar in action again, this time the dollar gained immense strength which sent oil down to ~$26.
Iraq's oil production is at an all-time high, and that oil belongs to them. They're currently directly competing with the vast US domestic oil production.
If the US had started the Iraqi war over oil, it wouldn't have willingly left Iraq when asked to, and it would have used its military to lock up all the oil contracts and supply coming out of Iraq, for itself and its closest allies, effectively annexing the oil. That didn't happen.
Halliburton share prices from 2003-2005: https://i.imgur.com/UgPNCBg.gif
NY Times article about the division of Iraq oilfields: http://www.nytimes.com/2011/06/15/business/energy-environmen...