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The first three are junipers of some type. Given your location and their general appearance, they all appear to be San Jose junipers, but it is really hard to tell due to the fact that they are stressed and are throwing tons of juvenile foliage (the prickly kind).
The next four are all Chinese elms.
The next one is a live oak. Probably a coast live oak.
Last one is a contorted Japanese quince.
I would also recommend Bob Pressler as a contact - he is right up in the Valley. However I'm not sure about house calls. You would have to call him and ask.
Kimura Bonsai Nursery
All of the trees are stressed. The soil appears to be bad - all are planted in potting soil and not bonsai soil. Potting soil compacts easily in containers and leads to oxygen-poor soil, water retention, root rot, and a whole host of other issues. Bonsai soil is usually free (or mostly free) of all organics. It looks like fine, sharp gravel. When your trees are potted in good soil, you water your trees and the water flows immediately through the soil and out the holes in the bottom of the pot - rinsing the soil and leaving wet (but not waterlogged) soil and roots behind.
If you look at your pots, you can see how the soil looks dark and completely solid - like swamp soil. It might even smell swampy. This isn't good. Additionally, given crappy LA city water, you can see all the mineral deposits left on the tree roots and the pot. This is a sign that water is accumulating in the soil, and then slowly evaporating, leaving all the salts and minerals behind. Eventually if you continue down this path, you turn your soil into alkaline desert soil (think the bottom of Owens Lake).
Normally you don't want to repot at this time of year, but given the condition of all of your trees, you will want to do so. I won't write a long article about repotting here, because there are tons of threads on it. Check the threads and ask any questions you want. Be gentle with the trees - it is likely they have not been repotted in years, and you may find they are completely root-bound in the current pots. If that is the case, you might want to buy some cheap plastic nursery pots that are slightly larger than your bonsai pots, pull the trees from the old pots, loosen the roots as much as possible and remove as much old soil as possible, and move the trees into the larger pots (with better soil) to allow them to recover before you worry about trimming/pruning roots.
Also, you might consider watering them a few times with distilled water from the store. You can usually buy distilled water from Target for about $.99 per gallon. Distilled water will not have any dissolved minerals, and have a lower pH than your tap water, and will help rinse the salts and minerals off the roots and out of your soil.
Because of their weakened state, after you repot you will want to keep them in bright indirect light but NO direct sun. If you put them out in July LA sun it will be the death of them. They will need light (no total shade) but no direct sun. Consider shade cloth sails to create a patch of protection if necessary. Also protect them if you experience any strong Santa Anas... same issue - their vascular systems are compromised so they don't have the ability to draw enough water up into the foliage to keep up with the desiccation rate of a strong dry wind. Protection is key. You will know your are out of the woods when you see new growth. The Chinese elms will be the first to bud - and may show new growth in as little as two weeks. The quince will be next and then the live oak. The junipers will take longer - perhaps a couple of months. Don't lose hope... just do the work and be patient.
Steve I'll call you this afternoon or early evening and we'll make a plan to rehab your trees. Bonsai Nuts advice is pretty spot on but we can fine tune as necessary.
