What can we do about previously filled holes so I can varnish wood?
Test it first. You may be able to just stain the filler as is.

If that does not work, dig out the existing filler with whatever tool works (putty knife, old drill bit, a thick nail) and replace it with something you can stain. Not sure if paint stripper works on filler, but it's work a short.

If there's any other stains or treatments on the door though, you need to remove those with chemicals like The Evil Greebo, and sand it down nice and fine.