When the emergency doors over the wings are opened do the wings automatically lower themselves, to allow passengers to slide and reach the ground? Or does the pilot have to do it from the cockpit?
Wings are static.
The wings do not move in response to emergency door opening. There is no requirement regarding position of flaps, in most cases involving an emergency evacuation after landing, flaps are likely to be extended, but I don't think this is guaranteed.
On commercial transport aircraft, there are marked routes on the wing for passengers and, if the exit point is more than 6ft from the ground, there are self-inflating slides that allow passengers to reach the ground.
Image from video by "Airline_Alex"
Evacuation on water
The inflated slides also work as life-rafts in the event that the aircraft comes to rest in water and has to be evacuated. Generally this applies only to slides at main exits, over-wing exits have slides that are not designed to be used in this way.
The regulations in the USA say
Each passenger-carrying landplane emergency exit (other than over-the-wing) that is more that 6 feet from the ground with the airplane on the ground and the landing gear extended must have an approved means to assist the occupants in descending to the ground.
The manufacturer must demonstrate that they can evacuate all passengers and crew to the ground within 90 seconds using only half the emergency exits.
This applies to aircraft capable of carrying more than 44 passengers.
Variations in arrangements by aircraft
Not all aircraft need overwing exits and slides. Here are some B757 variants
From CRJ Resets
As commenters have noted, the 737 does not have self-inflating slides for its over-wing exits.
The 737 system does not always work very well
Passengers climbed onto both wings, which were slippery due to the rain, but were able to see the markings indicating the direction of movement. It was difficult to see the ground in the dark and some passengers were not aware that they should slide down the flap surfaces. Others expected to find an escape slide. On the left wing, some passengers slid down onto the ground and assisted others. On the right wing, fewer people slid down to the ground, while others re‑entered the cabin and exited it using door escape slides when it was apparent that there were no visible signs of danger.
- from AAIB report
There are no transport aircraft where the wings would be movable.
However if you meant flaps, the question would make sense.
In most aircraft the overwing exits are equipped with inflatable slides that inflate aft over the wing trailing edge (see the image in the other answer). However in some aircraft it is indeed intended that the escaping persons will slide down the flaps, most notably on Boeing 737:
No, the flaps don't move automatically. The pilots have to extend them. Worse, the flaps require power to move and they move rather slowly, so they may not extend all the way due to lack of time or failure of the necessary systems.
I've seen some incident report involving evacuation where it was mentioned that the flaps were not extended all the way down due to lack of time, but I don't remember enough details to find the reference now.