Since your strings could be in a file other than string.xml, here's a more robust way to do this:
Take a string id that you know is translated into all your supported languages and test if it's different than the default.
    DisplayMetrics metrics = new DisplayMetrics();
    getWindowManager().getDefaultDisplay().getMetrics(metrics);
    Configuration configuration = new Configuration(getResources().getConfiguration());
    configuration.locale = new Locale(""); // default locale
    Resources resources = new Resources(getAssets(), metrics, configuration);
    String defaultStr = resources.getString(R.string.hello); // default string
    // lang is the two-character language code, e.g. "zh", "hi"
    configuration.locale = new Locale(lang);
    resources = new Resources(getAssets(), metrics, configuration);
    String testStr = resources.getString(R.string.hello);
    boolean supported = !defaultStr.equals(testStr);
    Log.d(TAG, lang + " is " + (supported ? "" : "not ") + "supported");
Note that Configuration.locale is deprecated since Nougat. See the docs for update.