How can I reduce the sodium/salt in Halloumi?

Soaking Halloumi might get rid of a bit of the salt in the cheese that's close to the outer surface, but it isn't going to do much for you. Chopping it up will increase the surface area and allow more salt to be drawn out, it's still not going to make it that much less salty. If you have concerns about salt intake then there is lower salt halloumi sold in places, however that doesn't taste like much.

A little halloumi goes a long way, you could just eat small amounts of it or pair it up with something else. I barbecued pineapple and halloumi skewers this past weekend with a 2:1 ratio of pineapple to halloumi and it was a very good balance. Everyone ended up eating one or two chunks of halloumi in the end, so really overall a moderate amount of salt.

An effective (if time-consuming) way to "reduce" the salt in cheese would be to make it yourself. Want less salt = add less salt.

Be careful about soaking cheese in plain water for too long. Cheese can get a bit slimy when soaked. I believe it is to do with calcium (and lack-thereof in the water).

As GdD mentioned, cutting the cheese in smaller pieces will increase the surface area and make this process faster, but instead of soaking it in water and lemon juice, soak it in fresh milk. The calcium balance of the cheese and milk will stop the cheese from melting as it would do in water.

Depending on the firmness of the cheese, you can leave from one to two days. If you're not satisfied after that and the cheese is still firm enough, you can change the milk and try for two more days and repeatable until it suits your taste.

You can also try to go for the lemon and water method, but then just add a teaspoon of Calcium chloride for every two liters of waters. I have to warn that I had more success with the milk though. Hope that helps!

Done this many times very effectively.

Slice and cover in (ideally hot) milk or hot water and simmer for up to 5 minutes in a frying pan on a low heat.

Water does soften the cheese, but I find that is no bad thing. Use a spatula to gently squeeze the cheese to remove extra salt / remove it faster. Replace the hot water or milk once with more hot liquid of the same to further reduce if desired, though I find this usually takes the process a bit too far. In your case you may want to as you're aiming for minimal salt.

If frying, drain the liquid from the pan, squeeze with the spatula and fry as normal on a medium heat, add a little olive oil if desired. Any residual liquid should quickly boil off and you'll find you get lightly browned. The end result is really good, especially with (unsalted) vine tomatoes which really help to cover any remaining saltiness - though obviously in your case, that wouldn't be the point.

You can't totally eliminate the salt, but this does work to get rid of 2/3 of it (ie. more than half it by taste) and I've done it many times. Even so I wouldn't rely on that being an exact reduction of salt by weight if you were consuming a large quantity, I suppose you could hypothetically dry and weigh the residue, but even that would contain proteins and be very inaccurate, not to mention pointless in a practical sense!

Hope that helps.

Also, others have asked to what extent this removes the salt.

A simple solution is to slice the halloumi into fry size pieces, add to the frying pan, half fill the pan with water, bring to the boil, simmer for a few minutes, drain the water, add oil, fry.