Diagnosis is going to show up on the licensing exam. It just is. And there's one big book that has all the diagnostic information you could ever hope to find: the DSM. Which DSM are you supposed to use? Depends upon where and when you're taking the exam. In California, DSM-5 questions will appear in December, 2014. For the rest of the ASWB-exam taking world, the exam will switch to DSM-5 in July, 2015.
The trick with studying diagnosis for the social work exam is that there's far too much information for you to possibly hold in one brain. It takes a giant, small-print book to get it all down. First step may be to throw away the giant volume and instead turn to the Desk Reference version ("The Desk Reference to the Diagnostic Criteria from DSM-5 (TM)," it's called). It's smaller, more to the point, and still contains more info than you'll likely need for the test.
Another way to approach the DSM is to focus on the big diagnoses. If it doesn't show up in regular social work practice, it's pretty unlikely to show up on the exam. Learn anxiety disorders, depression, personality disorders, childhood disorders. But set aside the obscure, the rare, and the stuff you've just never heard of. If by some chance that stuff shows up on the exam, sigh, take your best guess, and move on. Otherwise, you're overstudying, cramming your brain full of unnecessary facts, and generally making life harder than it needs to be. Got it? Get on it!