What did you mean by strategic? Do you have a theory as to why this invasion took place?
Strategic interests - large-scale, long term implications for the security and prosperity of a nation (generally). US strategic interests are served best by stability and friendly nations (not necessarily democracies) in the greater Middle East. The greatest threats to Middle Eastern stability who were not 'friendly' to the US circa 2001-2003 were (in order):
-Iran
-Iraq
-Afghanistan
-Pakistan*
-Lebanon
Lebanon was a problem only because it was used as a base for attacks on Israel, which the Israelis dealt with. Minor problem in the region.
Pakistan's government was ostensibly friendly to the United States, but US intelligence had long identified the ISI as being a potential haven for radicals, and the northern regions of Pakistan were known to contain some radical elements. But, Pakistan itself was taking action in those areas to a limited extent.
Afghanistan was invaded because it was seen as the only way to make a very public stand against the state-sponsored terrorism that resulted in the September 11 2001 attacks. Ousting the Taliban was the goal; staying for the aftermath was the unanticipated consequence.
Iraq, #2 on the strategic hit list, had an unstable dictatorial government that recently fought a war against Iran (and lost), then fought a war against Kuwait (and lost), threatened Saudi Arabia (#3 on the US oil supplier list), threatened Israel (one of the only functional democracies on the whole region and a US-friendly country), had used chemical and biological weapons on its own populace, and could easily be painted as a state-sponsor of terrorism even if it wasn't. The only reason the Gulf War didn't flatten Hussein then and there was because the UN limited the scope of the operation. Iraq was a thorn in the side of the whole region. Furthermore, the ideological conflict between Iraq and Iran was still simmering and could have resulted in open war. But, in 2003, the opportunity for military intervention in Iraq arose (based on some definite twisting of the truth, in hindsight). What the administration didn't forsee was that ousting Hussein would lead to a factional civil war in Iraq, which it did, and caused all kinds of other chaos thereby actually strengthening Iran...
...and let's face it, Iran is US enemy number 1, but they're militarily untouchable because they almost never get caught doing the things that everyone knows they're up to. Namely, it would (rightly) be seen as a war of aggression.
The trouble is that, despite a frightening similarity of religious belief, the governments and factions in Iran and Saudi Arabia REALLY don't like each other. Saudi Arabia is only rich and relatively regionally powerful because it is a major source of oil for the world - the whole Persian Gulf is, really. Disruption to that supply could cause economic chaos, and prior to the events of 2003 you had Iraq, Iran, and the Saudis all with extreme dislike of each other and all with respectably powerful (relatively speaking) military's in the region. Iran also has nuclear ambitions (likely for weapons as well as peaceful purposes). That's not good for US strategic purposes. There is no question that reducing Iraq's ability to cause trouble was a strategic objective. I also suspect that Iraq was actually practice for an engagement in Iran - Iran is friendly to China, China needs oil, China's government is full of pragmatists, Iran would dearly like to sell more of its oil, and an Iran with Chinese strategic backing is in nobody's interest. That part is conjecture on my part.
Nevertheless, the military interventions in Afghanistan have had a few strategic effects (I'm not judging these as positive or negative, they simply happened):
- Iraq is no longer a player in terms of regional imbalance. It's too internally conflicted.
- Persian Gulf oil supply to the world is therefore relatively safe, with the only actual threat being Iran and they aren't stupidly about to bite their only real source of revenue.
- The ability of radicals to hide within Afghanistan and support the logistics required to carry out another attack on the scale of September 11 has been eliminated. The pockets of Taliban and Islamic radicals are too busy fighting to blow up girls' schools and kill locals and Afghani/NATO military to worry about grandiose attacks on Western nations.
- The radical-friendly elements in Pakistan's ISI have been largely flushed out (evidence: bin Laden's death inside Pakistan).
- The primary locations of Islamic radical fighters have been pocketed into southern Afghanistan and northern Pakistan, are being constantly harassed by drone strikes, and pose no strategic threat to Western civilian populations or Middle Eastern regional stability.
- Large contingents of well-trained insurgents who got field experience in Iraq have now returned home and in some cases have successfully co-opted revolutionary actions. Libya, Tunisia, Egypt, Lebanon, and Syria have all seen the results of this. Egypt now has an Islamist PM, and Islamist forces will eventually take Syria. Hamas in Gaza has been bolstered with new weapons and experienced insurgents.
So, as we can see, while the invasions of Afghanistan and Iraq had a definite net-gain on US strategic interests in the Middle East, the law of unintended consequences is now at work. Actions of this magnitude are generally best reviewed with 20 years of hindsight to be properly judged. Regardless, Iraq's oil supply is little more than a footnote in all of this.