Found out that the Omega 2 Pro board microUSB port's data pins (D+ and D-) are connected to USB-serial IC. This means (if powered that way thru a PC) PC will interpret as a USB peripheral device and will power the O2 Pro board at most 500mA (sometimes even lower than that.) It will not supply most juice from it even PC's USB port is labeled as charging port!
This leaves not much headroom to power everything (O2S, Li-Ion charging function, and USB2 host port when a webcam is connected.)
This also leaves a dilemma that even if O2 pro's microUSB port is connected to a USB 2 power supply, such power supply most likely will not supply more juice (simply because the power adapter will detect there is a USB peripheral connects to it as opposed to a charging device connects to it.)
What to do? Use a "dummy USB BC1.2 or Apple Power enabler dongle" to trick the USB-based power supply to think there is a power demanding device connects to it.