I would say you certainly don't need TWO 70-300mm lenses. I
The 55-200 is half the weight of the 70-300, so might be worth keeping (and the 55-70 range would be useful too - but if you only had 18-55 and 70-300, the "gap" is nothing to really worry about)
The Sigma 70-300 isn't a true (1:1) macro, but if you're happy with it as a macro lens then keep it, but I'd consider trading that for a smaller, true macro lens like the Nikon 60mm - you'll get more magnification and sharper pictures.
All the lenses would work on a D5100.
The Nikon 70-300 VR will work on a full frame camera should you ever upgrade to one. The 18-55 and 55-200 (DX lenses) will not.