The central nervous system is comprised has both the volitional nervous system with includes the motor nerves and the autonomic nervous system (ANS). The ANS is the insensible nervous system. It controls things like digestion, heart rate and respiration. The ANS is comprised of two components. The Sympathetic nervous system (SNS) and the PNS or Parasympathetic nervous system.
The SNS is responsible the fight or flight response. It elevates HR, respiration, blood pressure, sweating. It’s preparing you to run from the saber tooth tiger. The ANS on the other hand is what is termed the rest and digest system. It lowers HR and respiration.
The SNS and ANS exist in a state of give and take. With too much hard training the SNS tends to stay jacked up too much and overpowers the ANS which can make sleep difficult. Extreme overtraining syndrome will end up with the ANS over whelming the SNS and chronic fatigue is the result. If you have not done so I recommend reading this. article I wrote or the chapters on OTS in our books Training for the Uphill Athlete or Training for the New Alpinism. There are 14 threads on this forum about OTS that you might want to read. See the index to the right.
I do not know of any way OTS affects oxygen delivery to the muscles.