Q.Nellie Stevens holly
On several of our bushes, we have a milky white, almost glue-like, residue mostly on the under leaf or stem.

It sounds like a infestation of Mealybug.
Neem Oil is a good treatment.
Here are a few links of Mealybug and other common issues.
https://www.gardeningknowhow.com/plant-problems/pests/insects/mealybugs-control.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm