I worked as a product engineer for 3 years for an o&g equipment manufacturer and was laid off earlier this year. I've been applying mostly to other manufacturing companies or to project engineer positions, but either don't hear back, or I find that the company is looking for engineers with design/drafting expertise (which I haven't done professionally) or industry specific experience.

Anyone have advice on how to move into other industries?

MEEN '13

Do a ton of research on the industry you want to go to (automotive, pharm...etc) and find a way your experience in O&G connects and translates well into the new industry or even give you a leg up on it

also, joining some professional organizations, taking classes, getting certifications wouldn't hurt either

Be absolutely certain that the resume you present, when applying for an opportunity, contains language pertinent only to their opportunity. Every word must lead the recipient to qualify you for that opportunity. If a recipient is reading your resume and identifies language that is far removed from the opportunity, the likelihood of receiving an invitation for an interview is diminished.

Best wishes.

Go get some design experience. Many CAD resellers hold free classes in their software that you could use to become more proficient.

Since you only have three years experience make sure you are considering every level jobs wherever you are looking.