Is it possible to have a cyst in your wrist that cannot be seen externally or on x-ray? severe wrist pain x4 mos, loss of strength x-ray ok

Cannot say: in your particular case without a direct visit/exam/etc. BUT cysts don't show up on x-rays. Irritations or damage of a nerve also does not show on x-ray. A tendon can have a bleb called a ganglion cyst; its symptoms generally are what you describe. http://www.mayoclinic.org/diseases-conditions/ganglion-cyst/basics/causes/con-20023936

Occult ganglion cyst: Yes, it is possible to have a hidden (occult) ganglion cyst in the wrist which might cause weakness. Ganglion cysts frequently cause a painful lump, and may lead to weakness and tingling when they push on a nerve. There are however, other causes of weakness. A visit with a wrist specialist (Orthopedic surgeon) and consideration of an MRI or ultrasound study would be the next steps.