Here's my attempt at laying out the strategy of this game:
Damage heals ONLY if at least one of two conditions are met while the submarine is surfaced (either via a mechanic or by surfacing near a supply ship on the maps that have them), but the inability to mask (turn invisible) while on the surface makes you vulnerable to homing torpedoes. Homing torpedoes are most often outdone by masking (turning invisible, which can only be done underwater), but sonar can locate you even while you're masked if you're not still, which will allow an actively engaged enemy to narrow down where you are. Standing still while masked, especially if you start being still before you begin masking, hides you from sonar but makes you a predictable target for people using unguided torpedoes. To dodge the torpedoes, you can move and/or mask, though moving predictably can lead to your enemy easily leading you as a target, but changing course too many times might get you moving too slowly to avoid already incoming torpedoes because you might lack velocity. For the best speeds when up and down, you minimize the amount of forward-backward thrust you're applying.
Outside of battle, some crew members that you can give your sub will tweak your sub's stats (+1 submerged speed, +1 health, etc., and all stats are out of 10, even as you level up), which can either improve already great traits of your sub, give the jack-of-all-trades starter sub some traits to excel at, or balance out submarines that have glaring weaknesses due to overspecialization. Still other crew members have special traits such as being able to show all of your allies on the map at the same time or slowly repairing your submarine's health for as long as you're surfaced. These will affect how you end up playing the game (I personally use my knowledge of where my allies are to figure out where my enemies probably are, and you'll probably see people who get repaired while surfaced take advantage of this ability even though surfacing makes you vulnerable as stated earlier).
Finally, you get the submarines themselves: the starting submarine is a long-range jack-of-all-trades submarine, which means that it can actually shoot many premium submarines from a range where they would struggle to shoot back, and apparently the long-range torpedoes are more powerful than the shorter-range ones! There's also the typical stats such as health, firepower, and speed, but firepower is instead divided into number of torpedoes, reload time, and range. Short-range subs often exchange having weaker torpedoes for being able to fire more of them before needing to reload all of them. Similar to the breakup in firepower, speed is broken up into rate of turn, submerged speed, and surfaced speed. Interestingly, the premium sub that scores a 9/10 in submerged speed scores only a 3/10 (even worse than the starter submarine) in surface speed. The opposite is also true, with a submarine that scores a 9/10 by default in surface speed only to score a 3/10 in submerged speed (I can only assume that this thing makes for a better boat than it does a submarine).
Aside from all of that, you only get a limited number of homing torpedoes (three per match) unless you destroy an enemy and find a homing torpedo power up in its place. When you destroy an enemy, you will get either a homing torpedo or a repair kit to repair maybe 1/10 of your health. Also keep in mind that you cannot respawn during a match and that friendly fire is entirely possible.
And that's about all that comes to mind for me with the strategy involved in this game, aside from mastering controls (Morse code chat, using your periscope, and remembering that throttles for going forward and backward and surfacing and diving are held in place until you move them, and getting used to how your turning control stick is shared with your surface and dive control stick, while forward and backward are buttons).
The strategy in this game is deeper than a submarine in the shadows of The Trenches.
Hmm, well I tried it. I completed the tutorial, the two basic missions and headed into an online match.
I was destroyed very quickly, everyone else had a much cooler looking submarine, and the match went on like 3 extra minutes while two subs whirled around eachother like turds in a toilet bowl. This game is not for me.
I would recommend going into a skill-based match. You should end up seeing mostly the same sub that you have.