[Wien1938]

Here's what I've found - the game makes a lot more sense when you pay attention to the sensor numbers. If your opponent gets a passive or active sensor number above 0, he's got an idea of where you are but he won't have you cold until it hits 10 or more.
When you launch a torpedo or a moss, you temporarily give your opponent a +20 advantage on his passive sensor scores (not the active, note!). So, what you want to do is wait until your opponent is at -20 or more on his passive scores and shoot then.
After you shoot, direct the torpedo away from your ship for at least 3KYD to give yourself some "deflection" and start slowly heading away from the target and your own torp.
At 3KYD (ish) your opponent WILL detect an incoming torpedo, so distance is an important balancing act between the ability to run the target down and his ability to detect your launch and/or the torpedo approach. Bear in mind that your opponent will launch counterattacking torpedoes on the approach vector of your weapon, so try not to be on that same vector.
Launch diagram (hopefully):
(You)----->
sea-sea-sea\
sea-sea-sea-\
sea-sea-sea /
(Target)<--

When caught by a torpedo, the best course of action is run away at full speed and use "knuckles" in the water to throw the torpedo off your scent and send it back into a search pattern. This buys you precious seconds to open the range and (works best with short-legged aerial homing torps) either get the little sod to run out of fuel and self-destruct or work yourself out of its sensor cone.
Once you watch its track turn into a circle, check the range to the other side of that circle. If the range is equal to, or, a little more than the known sensor range of the torpedo, you have a chance (pressing your narrow stern aspect) to slip out of the range. If the torpedo turns back into its circle, you've escaped. If it sniffs your trail and comes after you, use high-speed knuckles in the water and start the evasion process again.
Sometimes, you can't shake the torpedo, either because it is too fast, too close or sometimes the sensor is too good to be fooled. In that case, you're in for the fight of your life!
What I found (having read a bit on here and on Steam) to be most effective is to let the torp get to 500 yards distance behind you, then REVERSE course into the torpedo's path AND climb or dive at least 300-400 feet from your current depth. It's alarming but the advice is correct here - you can outmanoeuvre a torpedo in three dimensions.
Once the torpedo passes over or under your boat, turn BACK into its path, then reverse again towards the torpedo. This way, the torpedo cannot find you for another circle and gives you time to launch a noisemaker, break away for knuckling distance or shoot a MOSS on a course away from you but with a long angle to catch the little bugger's attention and give you time to go shallow or deep and stay out of its sensor cone. [EDIT: A tactic that I've used is to get above or below of the torpedo and circle under/over it about 400ft difference and wait for the blasted thing to self-destruct!]
If you have a passive torp that you can't fool, you're going to have to dance for a long time! [EDIT: This appears to be either when someone is wire-guiding a torpedo onto you OR where the game has bugged and a wire-guided torpedo has had its wire cut but the game hasn't correctly disabled the wire-link and the AI hunts you with a zombie sonar!]

Lastly, if in the far north, you can (I've done it!) use the ice to physically block a torpedo - they're not that smart!