Jeffrey, you can't be living on the noisiest street in LA, let alone Silver Lake...because we live on it. We have the same issue with roaring buses, loudly tuned chopper bikes, lively drunken crowds and melodious muscle cars all passing by our busy intersection in Silver Lake all at different parts of the day. I've described it as the "music of the neighborhood". But sometimes I've wanted just some peace and quiet and our original single pane, double hung windows don't do a darn thing to buffer much of the sound.
Sadly, what we've discovered talking to a couple of sound insulation specialists is that although you could install very heavy drapery, which would dampen the sound a miniscule amount, to really notice any real difference you'd have to make much more extensive changes.
Sound insulating windows are an option. These supposedly will reduce noise levels by 75-95% by creating a sound dampening barrier with laminated glass and a pocket of air. This isn't a cheap solution at $350 to $900 per window, but if you want something with drastic results, this might be your best bet.
The other thing you can do is add acoustic dampening wall coverage. We have friends who've mounted acoustic tiles onto canvas or hung up cotton batted stretched frames up on the walls to soften sound. But to be frank, the results weren't really enough for them to ditch their earplugs, even after they invested in the acoustic dampening material, thick curtains, and a heavy rug. Sadly, dealing with loud ambient outdoor noises is not a low cost solution problem, so you may indeed need to consider moving or investing in some sound canceling headphones.