Your memory is faulty, and we've been through this. There were a series of UN resolutions, each one incorporating by specific reference the others - which in sum gave Saddam X time to disarm and comply, failing which any member state or group of member states was authorized to act.
Henry's right on this one.
The authorization was not direct; there was no resolution saying, "The U.S. and friends can now take action", but there were the prior resolutions with the demands, worded such that even the lowest graduating law student fresh with his degree could hammer them together to make the case that the action was authorized. However much it may have been a case of bluster, with people saying, "Well, we didn't really mean that!", the words were there.
As for why we went, oil is an accusation by the left, trying to pin a profit motive on the right; removing Saddam is a feel-good justification for those who like to think of the U.S. as some sort of hero in shining body armor; establishing democracy is a pipe-dream piece of fairy-tale land spun out to make the democracy-worshipers bow down and sing Kum-Ba-Yah....
But the real reason is what Bush was insisting on so stubbornly through his last months in office: bases. Rumsfeld let it slip more than once, as well. It's part of the whole "New American Century" gig, a vision of a world run by the U.S., with all the nations which have resources our glorious leaders solemnly declare we need being held to the traces by the presence of high-tech American boys (and girls) on the ground, their hearts aimed always toward that beacon of freedom and hope.... blah, blah, blah.
Papa Bush got bases in Saudi Arabia and Kuwait. Baby Bush was supposed to get bases in Iraq. Israel may as well be a U.S. military base, so with a few more touches, Mighty America would have had a sword held over the Middle East, either to "protect" it for our interests, or deny it to others. It was imperialist doctrine at its worst, as bad as when the British Empire bribed one sultan to make war on another, so they could send in troops to provide "security" for a third, and get trade concessions from a fourth.
And to tie this back to the topic, it always puzzled me that Bush never, in those crisis days when America was whimpering and slobbering to Do Something, sought to have illegal immigrants offered citizenship through a term in the infantry. Colin Powell told Bush we couldn't put the needed numbers on the ground, however much Rumsfeld blathered about our technology and the capabilities of the U.S. soldier, so why didn't Bush put these two issues together?