I'll quibble a bit with @Gallifreyan's answer. Without giving anything away, Wednesday has no reason to flee from the new gods.
It was certainly a show of power. The vast amount of information provided were to impress upon Shadow how much trouble the new gods could cause for him. He is extremely important to both Wednesday's and Mr World's respective plans. They both want him on their side. This was Mr. World's way of pointing out how good they could make his life if he sides with them, and how bad they can make it if he doesn't.
Second, the gods each have their own flavor of magic. Wednesday is a god of war. His power comes from death and sacrifice. He's also a god of deception. His abilities are strengthened when he is sacrificed to, and those abilities are, in part, the ability to deceive. This is why he was able to talk his way onto a plane in first class without a ticket and why he was able to con a few hundred thousand dollars out of people with a uniform and a clipboard. That wasn't smooth talking, it was magic.
Similarly the new gods are only able to act through channels which are aligned with their nature. Media is able to control television, display illusions, mimic celebrity, etc. Her power is that of illusion. She couldn't physically overpower either Shadow or Wednesday. The Technical Boy utilizes virtual reality, high technology, and communications. It was probably his power which was used to supply all of the tracking information to the police. Physically the information at his fingertips is only useful insofar as it can be used to drive the machinery of law enforcement. Mr World has access to a lot of information, and he's certainly the leader of the new gods, but we haven't really seen any more than that. He's not a war god, he's not a god of guns or of death like Vulcan or Chernobog respectively. So he would have had no useful power in a motel room either.
So the answer as to why the new gods used the police is that their power is all indirect. They have the power to use the systems of law enforcement, government, and corporate power to act upon humans. But they don't have super powers like Laura does.