Supposedly there are strawberries that have been genetically modified but I've never encountered them personally. Matt is right about this, hybrids and gmo are two completely different things. Hybrids are natural sexual interactions, they occur in nature outside of human intervention. Genetic modification in the style touted by monsanto et al. usually involves taking the genes from a whole different biological kingdom (bacteria, fungi, animalia, etc.) and forcibly (often via infection with a specific virus) inserting them into the genome of the desired plant.
Researching the varieties of berries that will do well in your area is very important, many berry plants are dependent on very specific environmental conditions to thrive.
Edit: Just noticed the LA part of your post (duh) I'm in a similar climate so I'll peruse my
books and try to get back to you with some specific suggestions. I know that boysenberries are one of the easiest here on the coast in San Diego unfortunately I'm not very familiar with LA's nurseries.