The County of Santa Barbara allows construction to start at 7:00 a.m. (see the link below, section 9.16.015)
You may want to look into the City of Goleta's guidelines to see whether or not they are conflicting.
Without having more information concerning the construction permit I cannot recommend the "best way" to approach the landlord. However, if the construction next door is being performed at the request of your landlord you can certainly discuss an abatement of rent due to the inconvenience and disturbance of your quiet use and enjoyment of the property. With that said, I do not see any facts that detail a habitability issue, but rather more of a nuisance and/or trespass problem.
You may want to consult with local legal counsel and have a demand letter sent to your landlord. Best of luck.
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Many cities allow construction up to 7 days per week and from 7 am to 7 pm.
If your neighbor's construction is interfering with your tenancy, you need to contact you landlord and report it. You might also try contacting the city about the materials being left in your yard. If they damaged your cars, you will probably have to file suit against the neighbor and the contractors.