How to send commands (strings) from an Android device over to an ESP8266?
I just know one methodology. Using the wifi module, MCU should connect to the home network. TCP/IP Server has to be coded in MCU and it should listen for client connections. Android App will be TCP/IP Client which connects to this server. After connecting, the app or client can send TCP/IP data over air. MCU code will read this data and do necessary things like switching on LEDs etc.