Required to check-in in person at international layover airport

I am surprised SAS cannot do an OLCI for you for OSL to LHR. Make sure your passport details are all correct on your SAS reservation (on SAS's website). If that doesn't fix it, maybe telephone SAS to ask why OLCI is not working, perhaps they can unjam it.

In principle, the gate staff should be able to check you in and print your BP at the gate (although it will be a bit of a surprise for the gate handlers). If you cannot find a SAS desk airside, go to the gate as soon as possible, try to talk to the most experienced looking person at the gate, and potentially ask someone else if you don’t get a useful answer. Given the tightness of your timetable that is what I would do.

There is, or at least was, a bypass channel for non-Schengen to non-Schengen transfers, but it was under maintenance last time I was in OSL and before then you usually had to ask someone to open it for you. It's to your left as your approach passport control. It's a bit unusual to use it so you may have to attract someone's attention and ask them to open it. There's a long corridor and then a dedicated screening area, so it's normally fast, but you may have to wait for the screening personnel to arrive and open it up for you. Still, this is your best bet if you have a non-EU passport and there is already a queue of non-EU passports. The slowness of the non-EU lines should not be underestimated. You shouldn't have to present a boarding pass but you should know where you're going and which flight to catch.

Elsewise you'll go through immigration twice. If you don't have an EU passport you can expect to be queuing for some time because of the number of non-EU passports on that plane.

Check whether this is one or two tickets. KIWI sometime bundles two separate tickets and claims "Connection guaranteed by KIWI". If it's a single tiecket it says "Connection guaranteed by the airline".

If it's two ticket, you need to clear immigration and customs in Oslo and enter Norway. Make sure you have proper documentation to enter the Schengen area, depending on your nationality you may need a Visa.

Then you have to head to the terminal and go to the regular SAS check in counter, check in, get your boarding pass and go through security and exit immigration again. The process is no different from just starting journey in Oslo. Your previous flight makes no difference.

1.5 hours is on the tight side, but since you have no checked luggage, it seems doable unless your LAX flight gets delayed or you get snagged in immigration or customs.

I strongly recommend reading the fine print on KIWI's so-called "guarantee" and also check out a few online reviews of people who tried to use it. KIWI requires you to follow a fairly strict process and the guarantee has only fairly limited coverage, even if you do.