There are essentially two problems here, trust and sociability.
There is little you can do about your co-workers talking amongst themselves about non work related things in a language you don't understand. Many people would consider it rude, but obviously your co-workers don't. You could try explaining how isolated they are making you feel, but their is no guarantee that will do any good.
From your description though, I think that some people would consider your situation to be a Hostile work environment but taking any formal steps in that direction risks further alienating you from the group.
Getting them to include you in non work conversations is going to be difficult until they accept you as part of their social group, but that is far beyond the scope of a Workplace answer (books have been written on the subject).
From a different point of view though, I actually find it much easier to ignore people speaking a language I don't understand. When I just want to get on with work, I'm not interested in people nattering about the latest episode of some TV show or the Cricket results, so I'm happy to be left out of such conversations.
When you work in an environment where people speak languages you don't, you have to trust that they will speak to you about things which impact on your work.
If you are not being kept in the loop about issues which affect your performance, and you can't persuade them otherwise, then this is probably a problem that only your manager can deal with. If your co-workers refuse to communicate with you effectively, then it is probably not an issue that you fix by yourself.
One thing to do is to keep an ear open for words which have not been or cannot be translated. As a mono-linguist in a technical field who has worked all over the world, I can often tell what people are talking about things I might be interested in by the technical terms alone (LASER, programming language keywords, SI units and part codes etc.). Then it is simply a matter of checking "Excuse me, are you talking about X, is this relevant to my work?". Often this will cause the conversation to switch to English.
If you can identify when they are talking about things you need to be included in, then you can encourage them to bring you into those conversations. Often people switch back to their native tongue when communicating is too difficult or slow in a secondary language. I have often had to sit listening to people having a heated argument in a language I didn't understand, with only an occasional update from one side or the other. This is not a problem, as long as eventually you get all of the information you need.
This is a difficult situation, but if you can find a way to involve yourself in their social interactions, this may help all of your interactions with your co-workers.
More importantly you can try to learn how to identify when they are talking about things relevant to you, even if you don't understand precisely what they are talking about. The more conversations you need to be involved it, the more likely it is that they will default to your common language(s).
Finally, if you find that you really cannot get on with your team, and still don't want to take it to your manager, continue building better relationships with other teams, you may be able to make move into one of those teams instead.