SoftwareSerial Problem, Forwarding data to ESP8266 Garbage Output

It seems highly unlikely that you have a mySerial connected to the Arduino. Using instance names that make sense is not rocket science.

You are aware that only one instance of SoftwareSerial can listen at a time, right? You are aware that SoftwareSerial can't listen while it is sending, right?

Sometimes you really do need to use more capable hardware.