The refi was just a rate refi? No money was taken out?
Since you're in CA I doubt you have any equity anyway. I'm sure this is similar to your situation (regarding value) as our home dropped 54% from the purchase price. We had an offer to short sale, we had approval on a Thursday, but Friday the lien holder received notice of the bk and pulled the approval letter. Our short sale terms had a 15 day escrow on a CASH purchase and would've been complete and finalized before the court date, but the lien holder pulled the approval anyway.
About the bk; if it will take you longer than four years to pay off the debts, file for bk. Yes, a bk will hurt the credit (but in reality, who cares) but it will recover and you have the option to purchase a home after four years. A bk stays with you for 7-10 years, but that doesn't mean you wont have anything. What kinda terms do they offer on a negotiation; do you still get 15, 20, or 30 years? If not, I know that $50,000 debt paid over 5 years at a 4% rate is $920 each month. Paying $920 a month for 5 years is a heavy burden; according to the means test estimations ($63,000 2 person income <--as a reference point) you would be paying 15% of your GROSS, not adjusted, income. If the terms are 15+ - a bk will be off your record within 10 years.
And in California, the Homestead Wildcard is $23,000 + $3,000 equity for your car. Therefore, you can place $26,000 minus any liens on the vehicle to save your car. My household, two cars and a boat, which values are good enough that I was able to apply the wildcard, so I get to keep them.