E-verify and OPT

Im OPT in MBA field (not STEM) and living in VA. Can I legally work for a non e-verified company. I think I can but my DSO seems like they want me to find a new company that has e-verify. I have just 2 weeks left before my unemployed date be expired.

You need E-Verify for STEM OPT Extension. There is no such requirement for general OPT, but many recommend it.
Read https://www.e-verify.gov/faq/studentsuniversitiesinterns/am-i-required-to-participate-in-e-verify-in-order-to-hire-f-1