I am new to both android and qgis, but have 20 yrs experience with mapinfo and arc gis. I have installed qgis on a nexus 7 (4.2), but keep getting the error :
No qgis data provider plugins found in /data/app_lib/lib No vector layers can be loaded.
This looks like it may well be able to solve your issue:
I'm now experiencing the same "No qgis data provider..." error when building from source (also on Nexus 7 [Android 4.2]).
I've pasted the output of logcat for both the installation and launching of QGIS on pastebin here.
I used the .apk found here: