Call your bank and the DMV and make sure no one is messing with it.. also check your credit reports and file fraud alerts with all three and your bank.  

credit reports:  Experian, Equifax, TransUnion
http://www.consumer.ftc.gov/articles/0155-free-credit-reports

If it turns out to be not true, then file reports with the FTC & FCC (and your neighbor also) And probably should talk with the local PD and maybe file a report with them also.

https://www.ftccomplaintassistant.gov/
https://esupport.fcc.gov/ccmsforms/form1088.action

They called my neighbor saying that they bought my car from my bank for nonpayment and demand I turn the car over before they report as stolen since their name is now on the title...

Me too.  Say they are an investigator Bull crap!

Got a phone call from this number. The caller did not leave any message.