Is it true that the recent war conducted by The United States in Iraq was undeclared and illegal? Have there been any rulings by the US courts on this? What are the arguments for and against the legality of the war?
At no point in the Iraq War (or the Korean War, or the Vietnam War) did Congress issue a formal declaration of war. This is not unusual in present times; there have been only five wars (1812, Mexican-American, Spanish-American, WWI, and WWII) in which the U.S. actually did declare war.
Although Congress did not declare war, it did authorize the President to send the U.S. military into Iraq by passing a joint resolution. The idea that Congress can authorize a de facto war without formally declaring one is generally accepted; someone tried to challenge it in Doe v. Bush shortly before the invasion of Iraq, but the courts refused to hear the case. Use of military force without Congressional authorization is a far more contentious issue, but this did not happen during the Iraq War.
This also doesn't get into the question of whether the Iraq War was legal under international law, which is also hotly debated.
Article I, Section 8, of the USA Constitution says Congress shall have the power "To declare War", but the constitution does not specify how it must be "declared". For example, it does not say "By law" as is explicitly mentioned for several of Congress's other powers.
According to Wikipedia, only 5 USA wars have been formally declared by a law that uses "Declaration of War" in the title. The last one was WWII.
However, this is not required, and Congress authorized the Iraq war with Public Law 107-243.
The war authorization was upheld by federal courts with Doe v. Bush, 323 F.3d 133.
When the Authorization for Use of Military Force Against Iraq Resolution of 2002 was challenged in court, it was determined to be legal. The final resolution came when the case was dismissed in the Court of Appeals for the First Circuit, when the court decided that they cannot intervene:
In this zone of shared congressional and presidential responsibility, courts should intervene only when the dispute is clearly framed. See Nixon, 506 U.S. at 228-29; Baker, 369 U.S. at 217. An extreme case might arise, for example, if Congress gave absolute discretion to the President to start a war at his or her will. Cf. Clinton, 524 U.S. at 423, 425 (describing President's broad explanations for use of cancellation authority). Plaintiffs' objection to the October Resolution does not, of course, involve any such claim. Nor does it involve a situation where the President acts without any apparent congressional authorization, or against congressional opposition.
Internationally, (then) UN Secretary-General Kofi Annan called the war illegal:
When pressed on whether he viewed the invasion of Iraq as illegal, he said: "Yes, if you wish. I have indicated it was not in conformity with the UN charter from our point of view, from the charter point of view, it was illegal."
Mr. Annan's opinion is in no way binding to the US, but it has been brought forth as an argument against the legality of the war. That said the UN hasn't (to date) formally challenged the legality of the war, a process that would have to go through its Security Council, to which the US have veto power on.