Segment the oranges by slicing off the ends with a sharp knife. Put the orange on one end and cut off the peel and white pith. Segment the orange by slicing between the membranes. Remove the segments and drop into a bowl. Squeeze the juice out of the remaining membranes into the bowl with the segments.
With a knife cut each halved avocado half lengthwise into segments, cutting through the meat but not into the skin. Scoop the avocado meat into the bowl with the oranges.
Add the lime juice, shallot, grapeseed oil, and salt. Using a large spoon, gently mix all the ingredients together so that everything is coated and well combined. Remove to a serving bowl.