How do I refinish the exterior of a log home?

If it were my home I would be reluctant to have anyone power-wash it.  While a power-washer does a good job of knocking of the outside surface on wood, it pumps a tremendous amount of water into a structure, which as you know can cause even more trouble.  I would think your best choice would be the "old school" method.  Scrape and sand, then a wash to remove whatever is still on the logs.  You might want to look into some organic based "paint strippers" to dissolve the old varnish since I doubt you will get a good job going over this.  I would choose the most experience painter of the mix, since in this case you will want the most traditional sealing job you can ( oil-based materials)

Just don't power-wash, a bucket and stiff bristle brush with the garden hose to rinse will work just fine.