This is a difficult problem in many workplaces (including mine). You will need to be direct about what you want, why you want it, and why your request is reasonable enough that they should cooperate.
What you have already tried is understandable but is perhaps the worst possible approach-- it's indirect, unclear, and easy to overlook/ignore. Body language and arbitrary noises are not sufficient to express what you want, to the people to whom you want to express it, in a way that you can rely on being understood.
Someone might clear their throat or sigh loudly for any number of reasons, and the implicit setup of such actions is that it's 100% on others to 1) understand that you are unhappy, 2) with them, 3) for reasons due to their behavior, 4) that they can clearly identify and interpret, and 5) focus on catering to your happiness. Passive-aggressive signs do nothing other than express the face of your unhappiness, which other people may not care about very much.
Some people even actively reject such behavior, with the result that they will be even less likely to cooperate with you even when they perfectly understand your needs. It's much better to be direct and explain what you want and why the should help you to have it:
I'm sorry to intrude on your conversation, but I'm having some trouble focusing on my work due to some of the noise. I have to be here to get [tasks] done on time. Is there any way I could impose on you to speak a bit more quietly, or step outside?
As far as expressing why your request is reasonable, there are a few issues to keep in mind:
- This is a shared space, to which you have no more right than these
others
- A great deal of academic work is collaborative
- Noise may not be totally predictable
- It's easy to lose a sense of proportion in the face of something so
irritating to you
- You are a low-status individual in this organization
The first is the biggest problem. Unless it's clearly marked out a as a quiet space, your preference for it to be quiet doesn't necessarily override their preference to talk casually with one another. Especially if this is more of a once-in-a-while thing rather than an all-day-every-day sort of thing, it can be hard to clearly lay out how much noise (and how often) is too much.
In my own office I sit near a loud group of people, and they are loud pretty often. Their camaraderie is really important to them in that department. On balance they are significantly disruptive for less than 30 minutes at a stretch, and so on most days they are disrupting about 1/16th of my workday at most. It's not necessarily appropriate, but it's a hard sell to say that I can't get my work done due to that alone (there is plenty of other time, and plenty of other ways to arrange it). This is the case even though my productivity is compromised during those times, and some work tasks (like studying academic publications) are absolutely impossible for me in that situation.
The second bullet is a problem because working together is a crucial part of a lot of academic work, and developing and maintaining personal relationships is often an element of that. That doesn't mean that they need to do it in the office, but just because it isn't advancing your work doesn't mean that it isn't ultimately productive for the larger organization.
Predictability of noise can be an issue, especially if you are sensitive to it. For example, some people have loud laughs, and if they hear something funny it may not be a conscious decision to make that noise. They may intend to be quiet, but it just doesn't work out (for whatever reason). Sometimes what is meant to be a brief, meaningless, small-talk greeting becomes an inescapable conversation. It's also hard to evaluate noise in a meaningful way-- most people have no idea how many decibels it takes to be heard in different circumstances, so they can't know that they are being too loud for you without you telling them.
Losing a sense of proportion is a big issue for me. When I hear my loud coworkers, I go from whatever mood I was in to very annoyed in about half a second, and remain irritated even if the noise stops after a minute or two. It took conscious effort to identify that such a small portion of my day was affected by that noise, and my personal sense of grievance was too great for the actual situation. I am, simply, no longer a reliable assessor of how noisy they are being because my annoyance is now more of a habit than a true response to the situation.
Finally, as a graduate intern, you have very little pull in the office. This workplace is probably not intended to cater to you as much as the professors, and so the fact of your preference for more quiet will not be as impressive to them as your rationale for why more quiet is a good idea.
