First, let’s break down oils. There are plant-derived oils (essential oils) that contain secondary plant metabolites, which are basically compounds that can act as natural plant defenses. These essential oils have any number of insecticidal activities due mostly to the plant metabolites. Some of these effects are on insect exoskeletons, and some interact directly with internal insect pathways. There are hundreds of articles expounding on the effects of different essential oils on insects.

There are also paraffinic, mineral, or petroleum-based oils. I would probably lump soybean oil in with that group because—although plant-derived— it doesn’t contain significant levels of secondary plant metabolites. Paraffinic/mineral/petroleum-based oils affect insects in a few different ways, and interactions can depend on many factors, including the environment, insect, oil application, etc. Primarily, these oils affect gas exchange through openings in the exoskeleton called spiracles. They may block or partially block gas exchange to the degree that the insect suffocates or is unable to carry out other essential functions. The oil may also harden eggshells or break down the outer cuticle layer (epicuticle), resulting in not being able to hatch and reduced protection, water retention, etc. within the insect respectively. This is a brief overview that doesn’t go too deep into the science of it all, but here are some articles (in order of relevancy) that explain a lot more about different oils and how they affect insects:

Potential of the various oils for insect pests’ management and their effect on beneficial insects

Use of paraffin oils in agriculture and beyond: back to the future

Horticultural oils: possible alternatives to chemical pesticides and insecticides

Finally, there is little to no research regarding how soybean oil specifically affects insects. Since it is being looked to as a future replacement for petroleum-based oils, I would consider its effects to be similar, although it may be more or less effective than traditional petroleum-based oils.