The best reference for this is the section "pin sharing schemes" on pages 25ff of the MT7688 datasheet.
omega2-ctrl utility was obviously created from a corresponding utility for the Linkit Smart, not all of the pin groups actually make sense for the Omega2:
uart2group controls GPIO pins 20 and 21 which are not exposed on the Omega2
refclkgroup controls GPIO pin 37, also not exposed on the Omega2
wledare not relevant on the Omega2 either (these are for enabling ethernet LEDs and WLAN leds, all on pins not exposed).
What you could add to your nice diagram:
spi_s group is wrong in your diagram, the pins you labelled are the
spi (without _s = slave -> SPI master). However, omega2-ctrl does not offer switching these pins for good reason - SPI interface is used to connect the on-board flash chip so these cannot be switched while Linux is running.
spi_s are pins GPIO14..17, of which 14 is not exposed.
spi_s group is especially interesting, because these pins can also be switched to carry the otherwise unavailable UART2 (on GPIO16, 17) in addition to PWM1 (15). Unfortunately, omega2-ctrl in its current version omits this option. I fixed this and a few other minor things a while ago and posted it to onion as a pull request, but so far nothing has happened