A: This can be a frustrating problem. What you DON’T want to do is strip the head of the height-adjust screw by cranking on it with too much force. Try taking the entire bridge piece off of the guitar and soaking it in WD40 or some techs recommend a mixture of naphtha and 3-in-one oil. A small brush, such as a toothbrush, can be used to clean up corrosion and grunge. (Take precautions such as wearing gloves and eye protection and working in a well-ventilated space when dealing with these dangerous chemicals, please.)
After soaking and cleaning, carefully try to turn the screw. It should come loose. If it simply refuses to budge, you can try grabbing it from underneath with a pliers or vice grip; be forewarned that doing so will probably crush the threads. You may need two sets of pliers or vice grips or a vice and a pliers; one to hold the bridge piece and the other to turn the screw.
Unfortunately, getting the screw free may ruin it. Replacement screws are available in different lengths and sizes. Be sure you get the proper one to fit your bridge.