Do I have to install the April Cumulative update on the Application servers and all Web Front Ends??
If you aren't being affected by one of the issues the CU fixes, you don't have to install it.
But to answer your question, you need to install it on both the WFEs and the Application server. Any place where the Sharepoint bits were installed needs to have the CUs applied. WSS CUs should be applied first, then Sharepoint Server CUs, if applicable.