Movement and grouping strategy
Group your submarines together for two reasons :
- The more you spread them, the more likely one will get detected and destroyed. Indeed the area of one getting detected at any time will be directly proportional to the number of submarine "squads". Building submarines is expensive, losing one is like losing it permanently. During several trips this will be very damaging to your submarine economy.
- But most importantly, in case of contact you have more firepower, much more firepower. Firepower which can damage or even kill 0the enemy before they can hit you (long range torpedoes vs maws and tentacles, you know) This will make any encounter with "lesser" threats more easily manageable. With several submarines you can cover the vanguard's blind spots, too1.
However, like you don't put all eggs in the same baskets, don't put all your submarines on the same trip. Pairs or triplets are largely enough. You don't want to lose all your submarines at once when they meet good ol' giant Ch'Thulhu, and you might want to transfer several messages at different locations anyway.
Then, without knowing the threat, I'd advise to move near the surface or the opposite, near seafloor. You'll remove one angle of attack, one which is a big weakspot for your submarines. This also cuts the detection sphere in half2, reducing the risk of being found out. This and well, it will use the thermocline layer, as JamieB cleverly pointed out. If you can, choose trajectories closer to the equator, so that the thermocline is sharper due to the higher temperature difference.
Extend your detection range, know your enemy's behavior, keep your maps updated
Any tool to extend where you know your enemies are or will be is an invaluable asset. The more you know your surroundings, the easier it will be to avoid superfluous battles. Chart any previous engagment and detected threat, check for patterns and give the results to the next submarine captain so they act accordingly.
There is a caveat to the "detect as far as possible" approach however : Sonars work based on echolocation : This is an active detection system... Which can be detected by the very thing you want to avoid! If you know you are in a dangerous area. Stop emitting and use passive technology instead, slow down, and finally... hold your breath. I hope your heart can withstand the fear of the unknown :).
Create lures
Use autonomous submarines or special, non-explosive torpedoes as lures. They can be used to distract any incoming threat with something expandable. They should also be nice addition for recon' and vanguards for the same reason they can be lost with less cost.
Of course, they should use big speakers and play sea shanties to annoy them on low frequencies for greater coverage. The more attractive and tougher your lure is, the easier its usage. Alternatively, put a very strong explosive trap on the decoy, though note surviving Eldritch monsters will certainly remember it next time.
1 : I dismiss the responsibility for the following trauma in case the crew have to destroy another submarine to save their own skin.
2 : Effect lessened if you find there are now eldritch monsters digging in the ocean's sand or diving from above the surface. But that's an another issue :).