All multi-balls stack and can be started while any other multi-ball is in progress. In terms of scoring, they don't affect each other though. Shots aren't suddenly worth more just because you have two or three multi-balls going at the same time.
For Ship multi-ball, if Tortuga is ready, you can shoot the ship first, and then start loading Tortuga. But that goes wrong if you drain, so I think it's better to start Tortuga first, then start the ship once two balls are inside Tortuga. That way, you get to use the Tortuga ball saver to bash away at the kraken. (There is no ball saver for ship multi-ball.)
Once the kraken is dead, I tend not to shoot at it anymore. It's a lot of shots for comparatively few points. Instead, I tend to start either Heart or Tortuga multi-ball, and use the ball save time to work towards the next ship getting ready, as well as making progress on trunk and/or Jack, whichever is convenient.
If I'm in Heart or Tortuga and I'm down to two balls, a good option is to start a ship multi-ball. That acts as an add-a-ball and allows me to make more progress towards Heart Super Jackpot, or to stash more balls into Tortuga for multipliers.
For Jack, I tend to shoot at it mostly during multi-ball ball save time because that's safer. Once Jack is finished, I stop shooting at it deliberately, even if I have a chance to collect. There are not enough points there to warrant the risk.
Typically, I end up in the situation where I have one or two ships, and all compass lights except for Heart Super Jackpot and Davy Jones.
Assuming I'm chasing Four Winds (not a good tournament strategy), it now becomes an exercise in keeping multi-balls going and to use the ball save time as much as possible to make progress on the remaining ships and Heart Super Jackpot. In that situation, I try and start one multi-ball, and use the ball save time to make progress towards another multi-ball. That gets me closer to my goal (Heart Super Jackpot and Davy Jones). Ideally, I don't start two multi-balls at once (except for the ship add-a-ball) but let one multi-ball finish. Now I should be very close to another multi-ball. Rinse and repeat until I get to Four Winds…
For beating Davy Jones, the same strategy applies. Once down to two balls, if any other multi-ball is nearly ready, I focus on that instead of continuing to shoot at Davy Jones. That gives me four balls again and another ball saver that I can use to hopefully beat Davy Jones.
If I'm chasing points for a tournament, there is basically nothing of interest other than Tortuga over and over. Get to the point where the jackpots are maxed out at 2 million and keep grinding that for as long as possible. Put balls into Tortuga during Tortuga multi-ball for playfield multipliers, and shoot the chest occasionally to re-light jackpots. For maximum points, it is best not to stack Tortuga and Heart multi-ball. That's because, once a stacked multi-ball ends, I sit there with both Tortuga and Heart empty and have a lot of work to do to get back to a multi-ball. (Although it's fun to collect Heart Super Jackpot with a multiplier running.)
The South compass award (max jackpots) makes the game almost a one-ball game in tournaments. That's because, once collected, I can't get the jackpots back to 2 million again, unless I get to Four Winds, drain out of that, and still have another ball left with which I can start working on the now-empty compass a second time. With long balls, I can work the jackpot value back up to well over a million, but getting to two million requires 40 hits into the scoop (which I've never managed to do so far). And, as soon as that ball drains, the game resets the jackpot value back to 1 million; it's not possible to carry over more than 1 million jackpot value into the next ball. All this means is that, once the South compass award starts, most of the game points ride on that one ball.