If you want to know about Hugo Strange, you should watch the very fun "Batman: The Animated Series"
episode "The Strange Secret of Bruce Wayne"
. The character is goofy and played for laughs in the episode as he arrogantly presumes that he's smarter than Batman and ultimately gets completely tricked. It's very entertaining and even though Hugo is a bit ridiculous in it, based on the episode I can see how the character could be effective if played straight.
Whenever I hear about Hugo Strange, I always think of him as a guy obsessed with exposing Batman's secret identity. The only other experience I have with this character is a Batman comic audio tape I listened to as a kid, and in that as well, that same obsession was his defining personality trait. I don't know how close that is to his depiction in the comics, though.