Answering your question on the three poorest cities/towns in California will depend on how you define poor. Is it by poverty rate or household income? The Employment Development Department does not collect poverty rate or household income data? However, there are figures from the U.S. Census Bureau on poverty rates by cities and census designated places with 65,000 or more people. The most recent figures for California are from the 2006 American Community Survey (ACS).
The table shows that the cities with the highest poverty rates were Merced (28.7%), Lancaster (24.9%), and Compton (24.0%).
The Census also published figures on median household income.
The cities with the lowest median household income were Hemet ($31,749), Merced ($31,790), and Chico ($35,866). Of course, cities with less than 65,000 people could have higher poverty rates and lower median household incomes than the cities mentioned above.