If the Iraq War was because of their oil, has the US achieved their war aims

I'd say controlling oil possibly played some role in the desire to go to war, but it was neither the sole reason or necessarily the impetus to start the war. My analysis of why neoconservative leaders such as Cheney, Rumsfeld, and Wolfowitz were determined to war with Iraq was based on several factors. First, Iraq's location serves as a perfect buffer between major American allies Israel and Saudi Arabia, and Iran. A strong pro-American government in Baghdad would help to ensure that Iranian influence would be minimized in he region.

Also, many of the neoconservatives at the time were deeply influenced by the Vietnam war, which soured many American's towards the imperialist policy of the neocons throughout the 60's, 70's and into the 1980's. At the end of the cold war there was also a need to justify American military presence overseas and with the 9/11 attacks there was the opportunity to do so. However, this would require more than a police action against Al Qaeda and more of a full on international war. Given the mindset of the neoconservatives, I doubt the former was ever considered even if it were far more rational given that Al Qaeda is a non-state actor.

Financially, oil was probably less of a motive than the lucrative military contracts and expenditures that a war and occupation could provide. Furthermore, this was an opportunity for people like Cheney and his former company Haliburton, to not only make a killing off of an almost endless stream of government money, but to also remake the military in accordance with their ideological principles. A significant development in the U.S. Iraq war of 2003 was the privatization of the army. Not only in a non-combat contractor force to provide services (often at inflated rates), but in a massive mercenary force employed to protect state department officials and other security tasks. The latter also allowed the US to recruit soldiers from all over the world, even in countries that opposed the war. Even more frighteningly, the gray area concerning the legal status of mercenaries allowed them to perform tasks which were certain illegal and immoral. Mercenary companies such as Blackwater (renamed Xe and now Academi) do not have to disclose their activities as they are considered "trade secrets" and their employees only faced being fired even after it was shown that they would engage in insanely aggressive acts (such as running over traffic and opening fire on civilians) to dissuade any attacks on their state department officials. Given that the state department officials were the ones both being protected AND charged with investigating mercenary groups, Blackwater was able to avoid any serious threat from the US government.

Anyway, to answer your question, the war itself was not necessarily that costly to the US. The following occupation has proved to be extremely costly. Not only has the US spent a considerable amount of money and resources attempting to secure the country, but Iran wound up gaining a far greater degree of influence over the region than they have for decades (Iran was very unpopular in Iraq due to the very bitter and bloody Iran-Iraq war). The US did a lot to try and impose American (specifically neoconservative) values on the Iraqis, and took measures such as imposing their chosen political leaders and writing large portions of the Iraqi constitution. In addition to the flagrant abuses by the likes of Blackwater and the imposition of American military bases, this lead many Iraqis to take up arms and accept support from even Iranian associated groups. The Iraq war also played in with many of the abuses of the "Global War on Terror", severely damaging American civil liberties and freedoms.

This war was damaging in so many ways that it is hard to mention them all. There are a lot of good books on the subject from so many angles. I'd recommend Jeremy Scahill's Blackwater: The Rise of the World's Most Powerful Mercenary Army for the damaging effects of the military industrial complex and America's recent turn towards mercenaries. The late East Asian scholar Chalmers Johnson has a whole series of books (Blowback, Sorrows of Empire, and Nemesis) and a bunch of articles on alternet which detail the harm imperial overreach has on the US. Finally, a good book on getting the mindset which led to the American invasion is provided by Rajiv Chandrasekaran in his Imperial Life in the Emerald City: Inside Iraq's Green Zone.