The President does not need permission from Congress to legally go to war. It is a reasonable question to ask though.
The President does not need permission from a foreign body to legally go to war. It is a traitorous person who even considers the legal need for foreign permission.
Congress shall declare war...
This has always meant that if a president wants to declare war, he has to get their approval.
A declaration of war is not always necessary, however, but normally a president needs to get the formal support of Congress. Bush was very careful to get support, even when going into a situation where our enemy was not another state, initially, but terrorist groups and a couple of states (loosely understood, in the case of Afghanistan) that were thought to be supporting them. But he was actually was supported by Congress and everybody else when he went into Afghanistan and even into Iraq (which I think was not a bad thing but ended badly when we started kowtowing to Islam).
Clinton, the left's golden boy, had actually gotten all of his "authorization" to support the Muslims in Bosnia from the UN, which of course was completely manipulated by its Islamic members, and the Dems let Americans be UN troops.
Obama isn't having as much luck. This is partly because his obnoxious behavior has pissed off Europe and partly he doesn't understand Islam and doesn't realize that his being a Sunni supporter (because he believes it's the most anti-Western Islam) is upsetting other Muslims. He thought he would be their hero. But it's also because he doesn't realize that the Saudis want to keep the good times rolling for their princes and they don't want him to interfere with it.
The problem is that Obama, loose cannon in chief, could set off a true conflagration in the ME that could involve the entire world.