They look like Scale. It's a small sap sucker that has a harder coating/shell on the outside to protect it. Underneath is all the apparatus that does the damage. Brushing them off with a brush works without having to resort to chemicals. You might have to do it a few times to completely get rid of them.

Using chemicals can be counter productive as it does more damage to predators that eat the Scale than it does to the Scale itself.

Neem oil should knock it out.

If you can remove by "hand" I think thats always better.

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It's scale. I usually take them off with a paper towl and rubbing alcohol, then I powerwash with water and spray with neem oil every few nights for about a week. That should take care of them!
-Alex

I rub off as many as I can get off with my hands then blast the bits away then spray with something mild like insecticidal soap or neem oil every week or so until they are gone.
IMO they are pretty easy to control.

I knew what it was before I even opened your post, scale it is, and I agree with everyone here. Glad to see everyone recommending organic options first line! I would use a paper towel soaked in water first to remove as much as you can. I've used peroxide and alcohol first, but it doesn't seem to make a difference. It doesn't hurt, it just costs more than water.

Oleander is just prone to scale and mine constantly comes back. It's better to look for it proactively, I just treated mine, but it was just starting. Yours looks as if it's been there for quite a while. I also use neem, just make sure you apply it after the sun is off the leaves for the day.

Why not just cut off the infected parts of the plant? Oleanders grow like weeds, mine grow at least a foot a year even in pots. I have never had anything like that on any of mine, however. I have 6 potted oleanders, one of which is over 13 years old.

Cutting off parts of the plant always worked for a while for me, but never fully, unless I treated mine with neem oil, the pests always came back. When I first bought my oleanders, they had both scale and aphids, I sprayed neem oil on them one time and I never had problems with bugs again to this day and that was 3 years ago. But Oleanders love a good pruning so you may want to do that every now and again anyways after blooming. I pruned a few branches on my potted oleander this spring, my oleander in the ground has grown really fully so it hasnt needed pruning yet.
-Alex

Thanks all. Never had anything like this on any of my plants, inside or out, so I was a bit stumped. Pruning not really an option, otherwise, there will be nothing left. They are everywhere. Will remove and spray. No other plants nearby seem to have similar problem thankfully.