How can I turn off this water valve?
Typically this would be a quarter turn valve, and turning the key on the left would open the valve. It may or may not rotate 360 degrees, the design does not indicate that. Adding some oil or lubricant to all surfaces around the 'wing' cannot hurt.

If you are able to cut off the flow with the blue valve, try releasing the screw on the side of the Mueller. you may get access to the parts where you can lubricate it.  

It is evident that all of the metal parts of this system are deteriorated. If at all possible, cutting off the house at the blue valve and replacing the galvanized and using a ball valve cutoff would eliminate what will surely be additional problems.