I built an IoT weather thing based on this squixtech thing.  I had to do a bunch of modifications to the oled code to use my SPI OLEDs instead of the I2C OLEDs in the squixtech device.  I also used a ESP-01 board and had to break out the gpio by soldering directly to the esp8266ex chip. Video and pictures here for your viewing amusement:

I just stuck the ESP-01 and SSD1306 boards to the back of AAA battery holder with 3M VHB double-sided tape.  The batteries give just less than 3V. It seems to be enough. I also disabled the red LED on the 8266 board, it was blinding. You can see where i moved the current limiting resistor in the bottom left of the picture.

You can also see the pullup resistor I added to the enable line to get the module to work by itself.