Definitely a Euphorbia. Possibly a trigone (African Milk Tree). I grew one as a house plant until it hit the ceiling.
It cannot handle freezing temperatures. I have grown them up to 12 feet tall outdoors.
They are very easy to root from cuttings. Be careful of the white sap. It is poisonous and a great irritant to tender skin and the eyes. The sap bleeds as soon as you cut it. You can stop the sap from flowing by rinsing the cut end with cold water. let the cutting "heal" overnight and plant in a 3 inch pot of well drained media. Do not keep it over-wet, but do not let it dry out completely.
Be certain to wash your hands with soap and water after you are done.
Since it is almost reaching the ceiling, I would cut the tallest one. These plants can support many arms, so leave the arm it has. Cut it 3 to 6 inches above the arm and it will branch with more than one new arm from the cut. Make a cutting of about one foot of the top section for starting the new plant. You can cut the middle into more pieces for plants or just throw it away. Be certain to remember the top from bottom if you are going to use the middle section for it will not grow upside down.
I can try to identify which Euphorbia, if you want to make more photos. A close up of the white pattern and the growing tip will help.
The plant needs more sun if you can give it. I turned my indoor plant, 1/4 turn every time I watered it. Euphorbias do like to be watered regularly, and will make more leaves if grown wet.
Here is my E. trigone, growing outdoors
