First, here's the answer - I'm following it up right away with the details, just wanted to get it up here. :)

In this grid, the leftmost part of each cell is the nonogram, center is the Nurikabe, and right is the kakurasu.

This took me several hours. I did have other things to do today, but ah well, this was much more fun. Thanks for the wonderful puzzles. :)

In this grid, the leftmost part of each cell is the nonogram, center is the Nurikabe, and right is the kakurasu. For the nonogram, pink is fill and black is not, for the nurikabe green is fill and black is not, and for the kakurasu, orange is fill and brown is not. I swear there is a method to my madness.

*** Detailed Solution ***

The first step to this puzzle was to get as far into each puzzle as you could before you have to start going back and forth in between the original three puzzles and the slitherlink clues. Here's the state of each puzzle before you have to start comparing/guessing:

Nonogram:

Nurikabe:

Kakurasu:

Now, it's time to compare. Use the clues that you have to determine which few slitherlink clues can be determined definitively true or false. This is approximately a 50000 step puzzle, so I won't outline every single step, I'll just highlight some specific strategies that I used in each puzzle.

Nonogram:

Nonograms are my favorite. The important thing here is being able to identify which cells in a given row or column you are CERTAIN about. Sometimes that might only be one cell out of a three-cell block, because if the block is all the way left, or all the way right, the cell that is always covered is the middle. Does that make sense? This was the first puzzle I solved in its entirety.

Nurikabe:

The key for this puzzle was that the entire "sea" needs to connect. Without that piece of information you can't solve the puzzle without guessing I don't think. There's also a lot of "What if X goes here, what will happen to Y?" I even occasionally chose an inflection point in the puzzle, made a copy of my puzzle at that point, and then picked one of two possible directions. If that was wrong, then I went back to my "save" and started again.

Kakurasu:

This one was the hardest, and the one that took the longest. The key here was to start with the biggest numbers. 9+8+7+6+5+4+3+2+1 = 45, so for 40, each of 9, 8, 7, 6 HAD to be shaded. For 39, 9, 8, and 7. The rest of this is just going back and forth with the slitherlink clues, as there's not much you can do beyond guess and check without additional information.

Slitherlink clues:

While a clue being invalid doesn't mean that it's incorrect, the inverse is true. If the lines you're creating render a clue invalid, that's an extremely useful bit of information. If you have two out of three puzzles complete for a given cell, and they both match with the clue, if you prove the clue false, then the third puzzle's cell must be the opposite of what the clue dictates. I used this strategy many times throughout the puzzle.

Final nonogram:

Final Nurikabe:

Final Kakurasu:

From there, it's a matter of simply solving the slitherlink, which gets a bit tricky in the top-left but is ultimately the easiest part of the puzzle.