Bumps / sores / stripes on schefflera and rubber tree?
I'm so sorry that you are having this trouble with your plants! They appear to have scale insects. From what I can make out in your photos, the white scales are slightly bumped up with a darkish dot on the top which suggests scale insect.
Scale insects prefer shade so they are most likely to pop up on the part of your plant that is away from its light source. They multiply quickly. When removed, they leave a little mark where they have been feeding on your plant. (Those are the scars you have noticed.)
There are many different species of scale insect and they are all common on houseplants in our area. Some attack leaves, some just stems. They have needle-like feeding parts that they insert in the plant tissue.
To rid your plants of scale, you will need to remove them physically with your fingernail or some tweezers. Touching them first with rubbing alcohol on a cotton swab may help to loosen them but you should avoid covering the plant itself with alcohol. The linked guide to treating scale insects from Cornell Insect Diagnostic Labs can help with further treating this pest. Do not worry that the scale insects in the photo do not look like yours - there are many types!
Thank you so much! This was extremely helpful. We took a day and removed the scale from all three of the plants and then wiped everything down with dishsoap solution.
I expect I'll have to do a few more rounds until they're full treated.
I've been trying to figure out what was going on for quite a while actually, so I can't tell you how much I appreciate it.