You need to copy BOTH of these library files to your B4A additional libraries folder:

OSMDroid_3_0_8.jar
OSMDroid_3_0_8.xml

If your additional libraries folder already contains the (older versions) OSMDroid.jar and OSMDroid.xml then you should delete these older versions.

The 'library_resources' folder contains:

'library_default_resources' contains 'attribution_strings.xml' required if you plan to use the AttributionObject of OSMDroid. Copy attribution_strings.xml to your project's Objects/res/values folder.

'markers_balloon_overlay_resources' contains drawables and an XML layout that are used by the MarkersBalloonOverlay.
If you use MarkersBalloonOverlay in your project then copy these resources to your project's 'Objects\res' folder.

** All files added to your project's Objects folder must be set to READ-ONLY otherwise the B4A compiler will delete them when you compile or clean your project **
 