can motel management enter my motel room without my permission? What about police?

The police would need the motel owner's permission, if they don't have a warrant. They don't need your permission.

The motel owners (or staff employed by the owners) will have the right to enter the room whenever they want without your permission (because they own the property) but they would not be allowed to touch your belongings.

they are allowed to enter to perform routine maintenance or to clean it. In some jurisdictions, the police will wait until the maids come around and look through the open door, for any evidence of criminal activity (ie, "plain view").

You are however, still expected to have a reasonable expectation of privacy. So to avoid this, you should keep the "do not disturb" sign on the door; and also, keep the chain secured on the door.

Without the assistance of the motel management, the police would need probabal cause to get a search warrant or witness criminal activity to justify entering the room.

Yes. They can enter your room to clean or if you give them reason to check your motel room. They could also enter the room if you didn't pay your bill or if you gave them some sort of reason to throw you out of the hotel.

I'm not sure if it's the same everywhere but I'm thinking they can. I once woke up one time in a motel in San Diego with the owner of the place standing over me. I called the police and they told me it was in their rights.

Never thought too much about this