I am currently working with OSMDroid and try to display offline map using vector data that represented as .dbf, .shp, .shx files. I googled a lot but still can't find solution how to do this using OSMDroid. Can anyone help me? Thanks in advance.
OSMDroid is designed to handle bitmap tiles, not vector maps.
Have a look to Mapsforge, it could be more appropriate to your need.
You will have to convert your shapefile to Mapsforge. An entry point here.