As for the numbers in leu of the data the you expected. Try reversing the two wires that you are using for the Serial communications. I have this working correctly using the following:
All baud rates are set to 9600
SoftwareSerial esp(6, 7); // on the Arduino Mega 2560
Pin 6 wire from the Mega 2560 is on RX of the ESP8266
Pin 7 wire from the Mega 2560 is on TX of the ESP8266