They look like a mixture of a balloon back chair from the turn of the century and an 18th century (1700s) style chair. Maybe they were supposed to be a 1700s reproduction with kind of a "modern" feel. "Modern" 90 years ago, that is. Are you able to post a few more pictures of the underneath and/or the joints? In my opinion, you will spend more money refinishing them than they are worth. But if you are keeping them and want them to look good, then it is worth it to you. If you ever sell them, you probably won't make that money back. That one looks to be in pretty darn good shape. Maybe you could just ask the furniture guy to repair and conceal any breaks and do a few minor touch ups, for much less $$$.