Looks like the issue is still relevant. I've decided to buy ConceptDraw, cuz I able to load all Visio stencils and xml files there. Have anybody news about this feature in Omni?
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You can just copy Visio stencils into your stencil path now.
 

You can just copy Visio stencils into your stencil path now. If you download a Visio stencil you can do two things:

1. Just move it to your stencil directory.

2. File -> Open the stencil in OmniGraffle. When it opens it will prompt you to save it in your stencil directory.

The stencil works very cleanly as-is. It is immediately available, even for open diagrams. The only gotcha is that you'll have to add your own connectors to it.

James: OmniGraffle 6 shipped in September of last year, and contains the ability to import both the XML and the straight VSD Visio files. It also uses Visio stencils without modification.