The WeMOS D1 is a terrible attempt at making an Arduino clone. Get the WeMOS mini.
I see that the nodemcu takes a micro USB for power only. How do I go about powering the servos off it?
It should perfectly happy taking 12V on the Vin pin. Just like the WeMOS. Servos are to be powered separately, as always. The regulator on the board can't handle motors of any kind.
Do keep in mind that this are 3.3V boards, not 5V like the Arduino. That means that you can connect most sensors without level shifters, but also that some servos may not work (if 3.3V is too low a level for them). Also your MOSFETs need lower VGS(th), many logic level MOSFETs do not open well at 3.3V.