inoculate against (something)
To vaccinate someone so that they become immune to a particular disease (named after "against"). A noun or pronoun can be used between "inoculate" and "against." No, I never had chicken pox as a kid, so I've been inoculated against it. The MMR vaccine inoculates children against measles, mumps, and rubella.
inoculate (someone) with (something)
To vaccinate someone so that they become immune to a particular disease (named after "with"). The kids have been inoculated against measles, mumps, and rubella with the MMR vaccine.
inoculate someone against something
to immunize someone against a disease. We need to inoculate all the children against whooping cough. Have you been inoculated against measles?
inoculate someone with something
to use a particular substance in immunizing someone against a disease. Donna inoculated Richard and Nancy with yellow fever vaccine for their trip. She also inoculated Sam with something to prevent malaria.