Determining Power supply for my project

My project has:

  1. Arduino Nano
  2. 2x servo motors
  3. 1x MPU 6050

I am supplying power through VIN and GND, and I tried using a 3.7v 850mah lipo and a 9v battery with 800 mah but it still didn't work. Can anyone suggest the powersource I can use to power my project?

NOTE: I have a size constraint of 80mm x 30mm x 20mm (lxbxh). That's where the challenge is coming in.

3.7 volt must be too low.
What was that 9 volt battery? Technical data please.