The first thing to check is the setting for "Use English names in maps", found in Osmand Settings, General. If it is unchecked, native language should be displayed.
But looking at your screenshot, I suspect that your Nexus4 does not have a Japanese or East Asian font set installed. The empty rectangular boxes displayed instead of the Japanese characters indicate that Osmand is trying to display the Japanese, but your phone does not have the correct font.
You can check if the fonts are installed by going to:
http://en.wikipedia.org/wiki/Help:Multilingual_support_for_Android and click on "Check". It will display a list of languages, and show which ones your phone is correctly displaying.
If your phone does not have a Japanese font, the solution can be very complicated, and beyond my ability to help. Maybe others could help you with it.
Dan
On Friday, May 23, 2014 4:23:00 PM UTC-6, SteveMu wrote: