Can stress and anxiety cause severe body soreness, weakness, and muscle twitching all over constantly?

Yes, anxiety can: produce such symptoms but so can many other things. It is important that you see your doc. If he/she rules out medical conditions please see a mental health professional. Do not rely on medication alone but learn some self-regulatory procedures like self-hypnosis, self talk changing, etc. Peace and good health. Biofeedback may be helpful also.