What Micro 4/3 Lenses would I need to cover equivalent APS-C Lenses 10mm to 200mm?

Well, to cover it exactly, you'd need:

Wideangle: Panasonic 7-14/4 (optically much better than the Sigma, goes a bit wider) or Olympus 9-18/4-5.6 (not quite as wide as your Sigma)

As for the midrange, pick one of the following:

Fast zoom: Panasonic 12-35/2.8 or Olympus Four Thirds 14-54/2.8-3.5mk2 on adapter

Slow zoom: Panasonic 14-45/3.5-5.6

Collection of primes, pick whichever you want (all great): Panasonic 20/1.7, Panasonic 25/1.4, Olympus 45/1.8, Sigma 30/2.8. (I'd go with the 25/1.4 and the 45/1.8)

For the long lens, there is really no match. But you have a couple of options:

Olympus 75/1.8 is a *tremendous* lens which is equivalent to 100mm on DX

Panasonic 35-100/2.8 is expensive, and probably the closest to your 70-200, but a little shorter.

Panasonic 100-300/4-5.6 is pretty good, and *very* long.

Instead of trying to match focal lengths, though, I'd match purposes. Ask yourself what sorts of tasks you use your various lenses for, then go find m4/3 lenses that do the same thing. Do you take a lot of portraits with the 17-55? The 45/1.8 is a stunning portrait lens. Want a fast normal? Get the 25/1.4 or the 20/1.7. Just want a stunning sharp prime for cheap? Get Sigma 19/2.8 or 30/2.8. Want a long lens? 100-300. Want a fast moderate telephoto for fashion and standoff portraits? Get the 75/1.8.

m4/3 has far better primes than zooms, so you're going to go batty trying to "cover everything". Instead of that, figure out what you want to do, and get the lenses you need. You may wind up doing it with a slightly "not equivalent" lens set than you had on Nikon, but that's okay.

Here are in no particular order some m4/3 lenses for you to think about; all these are optically good and worth shooting.

Oly 12/2

Pana 14/2.5 pancake

Pana 20/1.7 pancake

Oly 18/1.8

Pana 25/1.4

Oly 45/1.8

Oly 60/2.8 Macro

Oly 75/1.8

Pana 7-14/4

Pana 12-35/2.8

Pana 35-100/2.8

Pana 100-300/4-5.6

Sigma 19/2.8

Sigma 30/2.8