I assume that unpaid money orders are subject to the same abandoned property laws as other bank deposits; am I correct? If so, after how long must they be reported to the state of CA?

Here is some info on CA escheat: http://www.sco.ca.gov/col/ucp/holder/index.shtml

Under CCP Section 1513(e), a financial institution is to escheat any sum payable on a money order that has been outstanding for more than seven years from the date it was payable, or from the date of its issuance if payable on demand, excluding any reasonable service charges that may lawfully be withheld and that do not exceed the schedules filed by the institution with the Controller, when the owner has not communicated electronically or in writing with the institution concerning the item during that time. (From Bankers Compliance Group.)

http://www.sco.ca.gov/col/ucp/lawregs/ucplaw.pdf
This is a great resource.