The best way to eliminate gypsy moth (Lymantria dispar) egg masses is to scrape them off the surface that they are found on, into a bucket of soapy water. What constitutes "soapy"? I would just say, as long as there are visible suds on the surface, then it is soapy enough. Alternatively, you could crush or burn the egg masses, once you remove them. If you live in a county where there are annual gypsy moth population surveys, you should wait until late winter/early spring to remove gypsy moth eggs. This will ensure an accurate estimate when the county comes through to count egg masses. There is usually no need for residents to spray for gypsy moth, except in specific situations where it is needed to protect a high value plant in a heavily infested area. You can read more about gypsy moth in this MSU Extension article:

https://www.canr.msu.edu/ipm/invasive_species/Gypsy-Moth/gypsy-moth-around-home

Staff did not answer my question - what is the proportion of oil, water and dish soap to spray on gypsy moth egg masses. Some of the material that I have read talks about a horticultural  oil such as golden pest spray.  But there is a homemade version - I just can't find the proportion. Old oak trees have very rough bark and it is impossible to scrape all of the egg mass without dropping part on the ground or leaving part on the tree.

I will reiterate that spraying of an insecticide is very rarely necessary to manage gypsy moth damage in a residential landscape. Mature deciduous trees, such as oaks, can sustain a great deal of defoliation from gypsy moth without lasting effects. If you decide that it is justified to spray an insecticide targeting these gypsy moth egg masses on your trees, then I would not recommend using a "homemade" pesticide. It is much more effective to use a commercial product that has been evaluated for safety and effectiveness by a third party such as the US Environmental Protection Agency. These products will carry a label with an EPA Registration Number. The instructions for mixing such products (e.g. Bt or horticultural oils) can be found on the product label. Always be sure to read the product label and follow all label directions in order to ensure the product's effectiveness, your safety, and to protect pets, family, and the environment.