In case people are still visiting for a working solution, here is what worked for me:– This is for Appcompat support library.
This is in continuation to ActionBar styling explained here
Following is the styles.xml file.
<resources>
<!-- Base application theme. -->
<style name="AppTheme" parent="Theme.AppCompat.Light">
<!-- This is the styling for action bar -->
<item name="actionBarStyle">@style/MyActionBar</item>
<!--To change the text styling of options menu items</item>-->
<item name="android:itemTextAppearance">@style/MyActionBar.MenuTextStyle</item>
<!--To change the background of options menu-->
<item name="android:itemBackground">@color/skyBlue</item>
</style>
<style name="MyActionBar" parent="@style/Widget.AppCompat.Light.ActionBar.Solid.Inverse">
<item name="background">@color/red</item>
<item name="titleTextStyle">@style/MyActionBarTitle</item>
</style>
<style name="MyActionBarTitle" parent="@style/TextAppearance.AppCompat.Widget.ActionBar.Title">
<item name="android:textColor">@color/white</item>
</style>
<style name="MyActionBar.MenuTextStyle"
parent="style/TextAppearance.AppCompat.Widget.ActionBar.Title">
<item name="android:textColor">@color/red</item>
<item name="android:textStyle">bold</item>
<item name="android:textSize">25sp</item>
</style>
</resources>
and this is how it looks–MenuItem background color is skyblue and MenuItem text color is pink with textsize as 25sp:–