More specifically I suppose it would be accurate to say that the Iraq war was not fought over oil, although both wars were not fought over oil. It would be difficult, at best, to assess the true motives of any leader in power at the time, or to prove the existence of a highly secretive shadow government controlling the U.S. and other world governments, manipulating each individual like puppets for some larger, grander nefarious scheme, particularly since such organizations would have remained so well hidden from the public, however, it would be possible to ascertain whether or not there was a reasonable pretext for an invasion on the grounds of acquiring a particular resource. The presence of said resource in the region, it's relative price or quality, where those resources were going after the war took place, the cost to gain ratio of the war to said resource, and many other factors could help display whether or not a country, and in this case more specifically the U.S., would have gotten involved for a resource, or oil.
While all I can prove is a distinct likelihood of the war not being over oil, the war most likely, had little to do with oil.
The Oil is not going to the U.S.
The oil not going to the U.S., it is going to France and China, two country's of whom actually initially opposed the war. [1][2][3][4] The United State's military along with civilian contractors set up oil rigs worth 9 billion dollars in the country, which are now under U.S. and Iraq military control. [1][2][3][4] The oil supplies are strictly under control of the government, and yet none of it is going to the U.S., which suggests that the U.S. has control of the oil, but is receiving none of it. However, a handful of U.S. companies may some meager profits, close to 490 million for Halliburton, which in comparison to the billions of dollars worth of the total oil supplies is a relatively small amount (and these were chosen in open bid contracts, meaning they weren't guaranteed profits as a result of the war).
Not surprisingly, the U.S. seemed to possess little interest in the Iraq oil. Inherently expensive, difficult to obtain and in relatively small volumes, Iraq oil would likely not be beneficial to the U.S., at least at our current point. Iraq currently produces approximately 2 million barrels of oil per day; as it's peak, Iraq produced 2.6 million barrels of oil per day. The U.S. consumed approximately 19 million barrels in 2013 [1]; Iraq oil could have, at best, contributed to approximately 14% of our oil supply, or X dollars, and as a result likely would not be of much interest. The U.S. has in comparison spent nearly 1.5 trillion dollars on the war; in the same time, X amount of money could have been made, merely a fraction of the money in return. In fact, the U.S. put many trade restrictions and Embargos on the oil coming from Iraq, and Iraq even claimed Kuwait was waging "economic warfare" by selling oil at cheaper prices than Iraq. At no point in the past or present has the U.S. truly expressed interest in Iraq's expensive, unstable oil reserves. It is difficult then to assert that the U.S. wanted to obtain the oil or would allow 800 billion dollars in assets put towards the Iraq war, and thousands of soldier's lives, to go to waste and not obtain the oil if they so desired, when practically nothing and no-one could stop them and it would be, on top of this, a complete waste of resources (as in, the cost would far exceed the potential rewards).
While one would believe that a quick google search could help alleviate the concerns regarding the U.S.'s interest in Iraqi oil, a common myth still perpetuated today is that the war was fought over, or for, oil. It would take a relative understanding of global economic, political, and scientific understanding of the importance of oil to truly grasp why such motivations were extremely unlikely to begin with, although, this can be somewhat easily explained.
Relative Amounts of oil
It would be an inefficient strategy to invade a country for a single Resource
Before simply explaining that Iraq has very little oil to begin with, it would be prudent to illustrate why such an idea would be illogical in it's own right. Initially, one must consider the impact that robbing an entire of a single, important resource would be devastating to that country, as a result, to obtaining that resource. While Iraq is far from as industrially developed as the U.S., roughly X percent of the population still have electricity, and large portions still use cars, and thus use oil. If one were to remove such a vital resource from their country, that is to cut off electricity or transportation, much of Iraqi urban society would come to a halt, causing a substantial amount of problems, including food shortages and in general a stand still of the economy, hampering the ability for the society to function. Large death tolls would begin to occur, and likely mass riots or protests to the oil confiscation would occur, destabilizing the region, and increasing the price of the oil as the U.S. would need to seek to defend it from, perhaps practically the entire country. Creating new enemy's, it's likely the U.S. would not only draw condemnation from the country, but potentially the rest of the world as well, and as a result could easily lose the resource.
Currently, the oil makes up approximately 1% (adfa) of the U.S.'s GDP. In most country, oil makes up a sizeable, but still relatively small part of the GDP. Even all the fossil fuels make up X percent of the GDP; invading a country for but a small fraction, despite all the cost for it, might then seem like a somewhat estranged idea. The strangeness of the action and it's ignorance of reality is likely more so the result of the convoluted nature of the conspiracy theorists ideas, and less so the supposed conspirators. Nevertheless, once the resource is obtained, it runs out, and becomes a finite resource, making it additionally difficult to justify such grievous costs for such a paltry resource (in the case of Iraq, x money, or x a year). What might be more reasonable would be to take a small portion of all the resources of the GDP; such as, 10% of the entire GDP. While it could anger the citizens, more likely a small figure such as this would be manageable, and the people would find it small enough to allow them continue. Furthermore, if a portion of the resources collected were given back to the people in the form of social welfare, such as healthcare, military or police systems, their concerns could be alleviated, and they may actually learn to like the individuals who provide them with such organized social welfare programs.
In fact, it wouldn't be all that dissimilar to the current tax system in the U.S. and other country's. If one were to invade a country, it would be best to preserve their over-all well being and try to win their hearts and minds, so as to provide more resources to yourself. You would likely meet little resistance if you appeared as if a liberator or at least benevolent. While some could now try to argue this is the case, it would at least not be for oil, and since the U.S. is receiving no Taxes from Iraq or any monetary benefit (actually donating money to Iraq, x billion dollars a year), this too is extremely unlikely. It does however, at least make more sense.
Saudi Arabia and Kuwait
There is a somewhat smarter argument that the U.S. felt their oil supply was threatened by potential damage to Saudi Arabia and Kuwait, allied countries with large oil supplies, and attempted to rescue them, then (potentially threatens by Iraq), almost entirely for oil. As stated previously, the actual volume of input or necessary production of oil from any foreign country's is rather low if not simply non-existent, however, there are additional reasons why we likely would not have invaded just to protect Saudi Arabia and Kuwait's oil supply. While such an argument would be one for a somewhat ambiguous side, now grasping at straws, supposing and assuming that the worst case scenario was true (in essence, a logical fallacy essentially pertaining to the "God of the gaps", in that there might be one possible scenario left where the U.S. might have invaded for oil, and thus it must be the case that they did), and there is the potential that it's true, there's no clear motivation or sane, logical coherent reason as to why the U.S., now motivated by nothing but pure greed, lacking a good will for man and altruism, or just a sense of common human decency, would have partaken in such an action.