How to determine device screen size category (small, normal, large, xlarge) using code?

You can use the Configuration.screenLayout bitmask.

Example:

if ((getResources().getConfiguration().screenLayout & 
    Configuration.SCREENLAYOUT_SIZE_MASK) == 
        Configuration.SCREENLAYOUT_SIZE_LARGE) {
    // on a large screen device ...

}

The code below fleshes out the answer above, displaying the screen size as a Toast.

//Determine screen size
if ((getResources().getConfiguration().screenLayout & Configuration.SCREENLAYOUT_SIZE_MASK) == Configuration.SCREENLAYOUT_SIZE_LARGE) {
    Toast.makeText(this, "Large screen", Toast.LENGTH_LONG).show();
}
else if ((getResources().getConfiguration().screenLayout & Configuration.SCREENLAYOUT_SIZE_MASK) == Configuration.SCREENLAYOUT_SIZE_NORMAL) {
    Toast.makeText(this, "Normal sized screen", Toast.LENGTH_LONG).show();
}
else if ((getResources().getConfiguration().screenLayout & Configuration.SCREENLAYOUT_SIZE_MASK) == Configuration.SCREENLAYOUT_SIZE_SMALL) {
    Toast.makeText(this, "Small sized screen", Toast.LENGTH_LONG).show();
}
else {
    Toast.makeText(this, "Screen size is neither large, normal or small", Toast.LENGTH_LONG).show();
}

This code below displays the screen density as a Toast.

//Determine density
DisplayMetrics metrics = new DisplayMetrics();
getWindowManager().getDefaultDisplay().getMetrics(metrics);
int density = metrics.densityDpi;

if (density == DisplayMetrics.DENSITY_HIGH) {
    Toast.makeText(this, "DENSITY_HIGH... Density is " + String.valueOf(density), Toast.LENGTH_LONG).show();
}
else if (density == DisplayMetrics.DENSITY_MEDIUM) {
    Toast.makeText(this, "DENSITY_MEDIUM... Density is " + String.valueOf(density), Toast.LENGTH_LONG).show();
}
else if (density == DisplayMetrics.DENSITY_LOW) {
    Toast.makeText(this, "DENSITY_LOW... Density is " + String.valueOf(density), Toast.LENGTH_LONG).show();
}
else {
    Toast.makeText(this, "Density is neither HIGH, MEDIUM OR LOW.  Density is " + String.valueOf(density), Toast.LENGTH_LONG).show();
}

Jeff Gilfelt's answer as a static helper method:

private static String getSizeName(Context context) {
    int screenLayout = context.getResources().getConfiguration().screenLayout;
    screenLayout &= Configuration.SCREENLAYOUT_SIZE_MASK;

    switch (screenLayout) {
    case Configuration.SCREENLAYOUT_SIZE_SMALL:
        return "small";
    case Configuration.SCREENLAYOUT_SIZE_NORMAL:
        return "normal";
    case Configuration.SCREENLAYOUT_SIZE_LARGE:
        return "large";
    case 4: // Configuration.SCREENLAYOUT_SIZE_XLARGE is API >= 9
        return "xlarge";
    default:
        return "undefined";
    }
}