$120k sales price x 3.5% down payment = $4,200. Closing costs would be in the ballpark of about $5,000 (lender/title+escrow/impound account for taxes/insurance). Right there that is $9,200 already. FHA loans do not require you have reserves, so technically you could be flat broke after that, but I don't recommend that be the case. I recommend you have at least 6 times your proposed housing payment in reserves *after* you buy the home - that way you can be prepared for any housing/financial emergencies.
With CalHFA you can get down payment assistance with California Homebuyer's Downpayment Assistance Program (CHDAP) or School Facility Fee Down Payment Assistance Program (SFF).
CHDAP is assistance up to 3% of the sales price - provided that you make a $1k/1% contribution from your own funds. So if you use CHDAP you'd have to put a down payment from your own funds of just $1,200 instead of the $4,200 mentioned above. CHDAP would cover 3% of the 3.5% down payment requirement that FHA has - your $1,200 would cover the remaining .5% + go towards your closing costs.
SFF doesn't require any contribution from you, but it's for newly constructed homes only and additional requirements apply.
You can read both handbooks (which are designed for lenders, but they carry a lot of information that the homebuyer should also be aware of) at http://www.calhfa.ca.gov/homeownership/programs/index.htm
In either situation (using the CalHFA programs or regular FHA programs) you can ask the seller to contribute towards your closing costs, called a "seller credit", which would reduce (and can completely pay for) the closing costs for the purchase.
So if you used the CHDAP down payment assistance, and ask the seller to pay all of your closing costs, you could technically get in a home by only having to put down $1,200.
You mention USDA financing not being available because the population is over 20k, and while pretty much the entire city of Los Banos isn't eligible, there are a few parts on the very edge of town which are.
You can view a map of which areas are/aren't eligible at http://eligibility.sc.egov.usda.gov/eligibility/welcomeAction.do
as well as you can punch in a specific address to determine if it's eligible.