I have added a PhaseListener to faces-config.xml:
com.project.NotificationListener
Before JSF 2.2, PhaseListeners are not registered as CDI injection targets. Using @Inject (and @EJB) has effectively no effect in PhaseListeners. You'd need to manually grab the CDI managed beans by programmatically evaluating an EL expression referencing the @Named's (implicit) name, or as last resort via JNDI and BeanManager which is quite clumsy.
So, if you can't upgrade to JSF 2.2 (which should be compatible with any JSF 2.0/2.1 and Servlet 3.0 compatible web application), then your best bet is programmatically evaluating an EL expression referencing the @Named name. Assuming that you've a
@Named("stuff")
public class MyCDIStuff {}
then this should do:
FacesContext context = event.getFacesContext();
MyCDIStuff stuff = context.getApplication().evaluateExpressionGet(context, "#{stuff}", MyCDIStuff.class);
// ...
If you can't go JSF 2.2 your best bet is to use Deltaspike Core.
It offers
MyCDIStuff myCDIStuff = BeanProvider.getContextualReference(MyCDIStuff.class, false);
Deltaspike is how you should get stuff rather then inventing that yourself. For example if you must have the BeanManager (for example to fire an event) then Deltaspike core also offers BeanManagerProvider.
http://deltaspike.apache.org/core.html