The first problem here is that they're using different versions of the support lib (android-support-v4.jars).
For the second problem, you have to use one of the Sherlock themes to get your project to run. ActionBarSherlock needs many definitions to get the action bar styled correctly. Thus it needs these styles and you have to use the ABS themes. You can use your own theme, of course, but you must use one of Sherlock’s themes as a base for yours. See the Sherlock theming guide for more information on this.
Change your AndroidManifest.xml file to use a Sherlock theme:
<application
android:allowBackup="true"
android:icon="@drawable/ic_launcher"
android:label="@string/app_name"
android:theme="@style/Theme.Sherlock.Light" >
<!-- ... -->
</application>