You do not specify the time between readings, so I assume that 1 reading every couple of seconds will suffice.
One approach is to have a sample and hold circuit for each variable you want to measure. This will reduce your errors due to skewing.
You could then capture 1 complete cycle of all your signals, saving them in memory as an array, sampling fast enough to accommodate any high frequency components in your waveform. Any distortion in your signals will probably be due to 3rd and 5th harmonics. Having captured 1 complete cycle your processor can now analyse the readinds and calculate the True RMS values. The time required to carry out these calculations will determine the rate at which you can scan all your signals.
You can perhaps reduce the calculation time by capturing and analysing only 1/2 of the waveform if you are confident that your signals are symmetrical, and I can't see why they would not be.
You have so many calculations to do that you may need to use a 51 variant with more 'grunt' that the standard 51.
Perhaps the easiest way to calculate your variables is to use the standard formulae and use a cross-compiler with a floating point library. Personally I would use Pascal and not even dream of doing it in assembly.
Good Luck

Regards,
Tony Gelonese