I have been working in strat consulting for 3 years, and background really varies. Many many of them have MBA and PhD in engineering, economics, physics, and mathematics. Few others have J.D., and very few of them have no graduate degrees (but significant years of experience coming from industry). Law background is very highly looked upon, because law school teaches case studies (what most strat firms do) hard-core.The biggest challenge for you would be to throw in your resume to get interviews. If you get to that point, you are all set.