Mathematical or emotional repayment

This is key right here: "Emotionally I should repay the loan to my parents first, as I know they'll then be able to help my sister buy her first home."

Consider doing just what you need on the house loan, and let that ride. Interest rate is decent, and the other two have much sooner payoff timelines. You can keep picking away at the house loan while eliminating the two smaller loans.

If you haven't already, I'd suggest sitting down with your parents and talking this through. You're evaluating how best to prioritize paying off debts, and are examining whether to pay off the student loan faster or the parent loan faster.

A consideration: That's great that you're wanting to keep in mind your parents being able to help your sister buy a home. But is that a hypothetical, or is your sister starting to move her life in that direction? That's a key factor, right there. If she is moving that way, I'd see the case for accelerating paying the parent loan.

If things are on track with the parent loan and they are satisfied with where things are, or your sister isn't yet ready to buy, though, that student loan payoff has all the markers of being your primary goal. It's got both the smallest amount owed, and the interest is similar to the home loan, just a nick over 5%. The 170 000 NOK is about $17,848 USD. Paying that off frees up a nice chunk of change.

I'd suggest you consider aggressively paying off the student loan first, then upping your repayment of the parent loan. It helps you more on the straight-up math side, other repayments are continuing, and you both pay off an entire debt, then can accelerate your payoff of the debt with the most emotional consideration.

If your sister is getting closer to her own journey as a homeowner though, that could merit paying off the parent loan first.

Looking over your situation, I'd suggest that's where a conversation with your parents is key.

It's clear that you're doing the right thing, it's just a matter of which strategy is best all around. I'm confident they'll see that, respect where you're coming from, and support you in picking the right loan to prioritize first.

IMHO, pay your parents back first. I think they will do the most good with the money and they are not "in the business" of lending. It would also help out your sister. After that, I would use everything you were paying your parents to add to the student loan and pay it off, rolling the total you were paying that lender into the house loan.

But, that's just me and I hate debt, especially family debt. Some people would have you pay the debts as agreed and invest everything leftover.

Which I might consider with the house debt. Paying extra on the principle of the house reduces the debt, but doesn't help if something happens and you can't pay the mortgage for a few months. Even if you have paid an extra five years in principle, the mortgage company can/will foreclose and you would lose all of that money.

If you invest the money you would be paying toward principle and something happens you owuld be able to use that money to pay the mortgage payments and would not be in arrears. Once your investments equal the payoff, you can choose to pay off the house or just let it ride and pay it as agreed.

In our case, we paid off the house. That was in November 2019. The Covid hit. I was glad to have a paid off house. I had retired and in March of 2020 the US stock market took a big tumble. It was only for a month or so, but we didn't know that at the time. It felt good to know that the house was paid for. The rest of the bills were only like $300 US per month (not including food) and my wife was still working part-time.

How do your parents feel? I'm not asking what they SAY but how they'd actually FEEL. Would they be prouder if you paid them back faster? Would they feel resentful if it took longer?