I tried to create a Screencast to demonstrate what I was successful with but for some reason Screencast is currently failing to start for me. I'll try to describe it along with the picture below. It's helpful if the sketch only contains the SVG data or if the SVG curves are away from any other sketch entities so that they're easy to select without getting other curves too.
Here's a quick way to determine if what the steps were successful and you'll be able to move the result. Just try moving one of the curves from the SVG import. Initially, you can't. Perform these steps to allow them to be moved.
- Drag the mouse to window select all of the curves that were created by the SVG import.
- Right-click on one of the curves to display the context menu and choose the "Fix/UnFix" command, as shown below.

Try dragging a single curve now. If you can drag a single curve, the "Move" command should work and allow you to move all of them at once. I had some weird behavior if I accidentally got another sketch curve in the selection when I was trying to "UnFix" the curves so if it doesn't work the first time, try it again being careful what you select.
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Brian EkinsInventor and Fusion 360 API Expert
Website/Blog:
https://EkinsSolutions.com