I guess these are eggs of some pest which is infecting the kale and strawberry plants in our garden. Has anyone seen something similar to this? If yes, what did you do to get rid of them without any use of harmful pesticides?
I don't think those are eggs. I think they are aphids.
Put your gloves on and squish them. It will be easiest, and little is in fact lost, to just remove heavily infested tissue, such as the leaf you show; crush it as you discard it.
A jet from your garden hose will usually remedy problems before they become serious if you just make a habit of 'blasting' the foliage when you water (or doing it periodically if you are using an irrigation system instead of hand watering).
Aphids siphon off the sugars from photosynthesis, so you'll find them most prevalently on new growth and along leaf veins. If 'squish & blast' doesn't keep them at bay, it may be necessary to spray a pesticide such as NEEM to get back in control (comply with the label instructions!).
Those are aphids. Aphids come in many colors including gray, black, red, yellow, green, and brown. And I've seen them turn orange in the fall (after a frost I think) on a plant I had.
- Spray with soapy water so they come off.
- Or cut off the branch and burn it.
- Or place the branch in a capped jar of alcohol for an hour. Then put branch in garbage, do not compost in case there are other pathogens on that branch.
- Make a solution from tobacco, the cheapest you can find. Put a handful of tobacco in cheese cloth, tie with a string. Soak it in 2-3 cups water for 24 hours. Strain into mister bottle and spray. The nicotine kills many types of insects. If you are concerned, wait 1-2 hours after spraying and rinse with water to help out the pollinators.
Possibly caterpillar droppings. See this link. Aphids are usually underneath the leaf https://www.eatortoss.com/yep-that-greenish-dirt-on-your-kale-is-caterpillar-droppings/