What is better approach of the following in designing an Android app
res/values/Strings.xml
or I imagine a constants class would be more efficient.
However, speed shouldn't really be an issue in either case. I would recommend organizing based on what makes sense.
Constants class
Put strings constants that will be used internally, like database column names or other keys.
strings.xml
Put strings that are displayed for the user. This way you can take advantage of localization, etc.