Every step I take I can hear a loud dull thud because of Shepard's footsteps and it is starting to get on my nerves. Is there any way I can turn this off without impacting any other sound in the game? Perhaps there's a way to modify one of the .bik files or a mod or something?
Even if you could find the file(s) it may be trickier than just replacing it with a blank. You need to figure out first whether each environment is a separate pre-rendered file, or if there are a few files being rendered on-the-fly.
I've removed individual sounds and animations with some success in other games. Specifically, I tend to remove spell-effects in MMOs to reduce lag.
Assuming the first case, you may have some luck. If there is a separate "steps in water" file and "steps with echo" file, you could well be able to do what you're asking. Even if you can though, you should do a little research to see what Origin does regarding check-sums on your game files, as modding may throw off your game enough to get you kicked or banned -even if it's not cheating.
If the second case is true, then the short answer is, unless you are a hardcore programmer, it's probably not worth your time. But it's an interesting thought, and I may look further into this one if animations/sound become a problem in multi-player. Most likely the only work around is to lower SFX sounds and you would definitely be losing other things if you choose that option.