Oleander shrubs can be started from cuttings if you follow a few simple steps. This is a guide about starting oleander from cuttings.
How do I start a new plant from Oleander cuttings?
Hardiness Zone: 8b
By Deanna from Mojave, CA
In Phoenix, 40 years ago, I did an experiment for a university lab where I bundled oleander cuttings and buried them upside down like some old textbooks recommended for moving grape cuttings over great distances. I got about 70% success after planting them upright in the spring. Good luck.
The method I used is quite a long process so you might not want to use it. I took cuttings from fairly new growth and then put them individually into dark bottles with filled water, but not letting the cut edge touch the bottom of the bottle- you need to change the water frequently as it goes yukky and the cuttings rot.
After a while the cutting will sprout roots, I wait till the roots are a fairly good length and then transplant them into a potting mix. Then I leave them to establish a strong root system before hardening them off and planting them out. I've had fairly good success with this method. I did lose one through impatience though as I didn't give it enough time initially to grow some roots in the water.