Some very good advice given in previous answers
I have one point to add. One thing that helped me a lot, was realizing that when my radioman shouts "wasserbomben!", it does not necessarily mean that the depth charges are anywhere close to the boat. When I heard "wasserbomben!" I always put on flank speed and made a hard 90 degree turn - and thus gave my position away to any destroyer listening.
Now I keep listening to the hydrophones myself and try to find out if the destroyer is actually over me. If the hydrophone bearing moves quickly, even so quickly that I lose the destroyer's position, he's close and I have to be ready for flank speed. If he's close, you may hear his engine screws in the Zentrale room (F2 room) too. Many times they just waste depth charges having really no clue at all where I am. No need to panic if you know there are no destroyers dangerously close to you. Just keep on going silently.
The depth charges need to be very close to you to damage you. These thoughts apply from 1939 to March 1942. I have only played that time period yet. I haven't really played vanilla SH3 either, only GWX.
