Not only that, I think that a person who has an accent and speaks English imperfectly, yet carries himself confidently, is particularly intriguing to many people. They're often more interesting than the normal confident guy, because there's an element of mystery. "This guy is really cool and is probably popular where he came from. I bet he has lots of interesting stories to tell about things I've never experienced."
Also, foreignness is probably the best conversation starter that I can think of. People love asking about where you came from, and if it's true that so-and-so happens there, and what do you like about America? People LOVE teaching the basics about their culture to curious foreigners, it makes them feel like an ambassador.
There's so much you can ask other people ("how does X work here", "Did you grow up doing Y?"). If you can't think of something to talk about, talk about food. There's a million conversations you can have about food to someone from another culture.
In short, don't feel intimidated by being foreign - it can be a huge advantage to you once you get confident!
Now I am in my 30s, but when I was 24 I left my home country in Europe to work for an year and a half in the US, then moved again to another foreign country (UK). Work was great, but it was really difficult to meet new people, not to mention girls. My English wasn't good and I didn't know anybody apart from my colleagues. So I learned it the hard way: I enjoy photography and I got into a local flickr group. Doing photo walks allowed me to get in touch with different people with the same passion as me, without having to think too much as the way I used to speak. The "walks" allowed me also to walk by with one person at the time, avoiding the awkward moments when you are supposed to talk in a table where all the other people can talk easier than you. I also met a good bro who I still see quite often! And when bored, I could ask him if he wanted to go to the cinema, to have a beer or to see an art exhibition. Few years later we even got into talking to some girls in bars. That didn't go too far most of the time, but it helped the self esteem and I could feel better when talking to random people. I also started rowing (but you could try another team sport). It was a beginners' team, and even if I left it in the end I really think it boosted my confidence to hear the other guys support.
Also, I really think you can improve your English by watching TV and films. And learning to drive/having a car might inspire you to join interesting activities (my experience says that the US can be a difficult country to live in without a car).
The one thing I might at is about girls: it's a chicken and egg problem here. You get good with girls by talking to them. After my first girlfriend I felt like I could talk to almost all girls now.
So if you weren't so lucky as to grow up with female family members, start by becoming friends with girls even if you don't find them attractive. Especially so, since you won't feel the extra pressure. Eventually it will all bear fruit.
It's a long journey, but the sooner you start the more time you will have.
Firstly, it sounds like you are prioritizing school/work above yourself. Remember that work and your education are a means to and end. That end is having a fulfilling life and finding happiness. Now, I don't know you so your goals may be different (e.g. you may seek spiritual enlightenment) but for most people, happiness is what they're after and many don't even realize it.
Humans are social creatures, which is why social isolation is hurting you so much. The way we've evolved physically even indicates this. For example, the whites of our eyes are more exposed than any other creature including primates and the color difference between our pupil and iris has a high contrast. This is so that others can see what direction we're looking in - it's a form of intra species communication that we've developed because we're such social creatures.
Now, on to solving the issue of isolation.
I'm 40 years old and it took me the first 35+ years of my life to realize how you make friends. It's quite simple:
You make friends through shared experiences and the more intense and prolonged the experience, the deeper the friendship.
That's it. So lets test this:
Think of the best friends you have made throughout your life. They are school friends, friends you did intense activities with, took risks with, got into trouble with, failed with or had successes with.
For me they are surfing buddies, people I worked with at startups during the dot-com boom (including my wife), people I climbed mountains with and so on.
I'm sure many on HN can vouch for this.
So assuming the above is true: That you make friends through intense shared experiences, the problem you're facing becomes relatively easy to solve.
You're not going to make friends by going to a pub or standing on a street corner.
You might not make friends in your internship because you're just too busy to interact or it's not that kind of job.
You mentioned that you have weekends - and you currently dread them. So take those two days and put yourself in situations where you have intense experiences that you share with others.
You might join a mountain biking club and do beginner rides with other beginners. Or if you're not physically active, join an ethical hacker group and try to qualify for the DefCon capture the flag competition with other hackers. I don't know what your interests are, but putting yourself in situations where you're having intense shared experiences with others is what you need to do. They don't have to be throw-yourself-out-of-an-airplane intense, but riskier experiences are better at forming deep relationships in my experience. So take a few risks with others. If you don't already have friends, joining clubs is the best starting point I think.
Now, about those girls you want to meet:
The best way to solve this is to get a car. If you're in california you MUST get a car. You are not going to get laid if you don't. Simple. Trust me on this - I was a 20-something in Southern California working for a tech company once. If you can't afford one, rent one on the weekends. Make a plan. But get a car.
Secondly: You need to make a few bros. This sounds ridiculous but the best way to meet girls is to get a few guy friends. You need social proof. You need a few bro’s to vouch that you’re not insane, creepy or dangerous and to bring you into a circle. So start by solving the problem of making guy friends. Through your guy friends you will inevitably meet a few girls and they’ll realize you’re OK because you’re with guys they know and things will start to happen.
And get off Facebook. A wise man I know once told me that the less you have going on, the more you’re on Facebook. Get out there in the real world and start having some cool experiences with other people and you’ll find that the rest starts to take care of itself.
And regarding your accent and ability to speak English: Don’t worry about that one bit. Pretend the problem doesn’t exist, hold your head up high and just communicate in your own way. Believe it or not there are people out there that think that foreign accents and English learners are cool.
One last note: If you have trouble joining clubs or getting into groups to do things, don’t let that stop you. Just go out there and do stuff on your own. Go for a hike on a popular trail and force yourself to engage people you meet. Ask them for directions if you have to even if you know where you’re going. You’ll find there are plenty of friendly people (I’m one of them) that will ask you to join them on the hike for a while and start chatting with you.
I wish you the very best of luck.
Edit: I wanted to add: Some folks have recommended Cialdini's "Influence" as a book to read. Be careful of some of the stuff he teaches e.g. Reciprocity. If you keep doing people favors as Cialdini suggests you will actually find you are resented to a certain degree. As someone else here mentioned - having people do YOU favors is a more effective way to gain friends - and make sure you then return the favor but don't overdo it. Also "How to make friends and influence people" is another book to be careful of. For example he teaches to memorize someone's name and use it. Well guess what, every car salesman out there has read this text and if you keep saying "Mark" this and "Mark" that, I'm going to think you're a sleazy car-salesman-type and avoid you - and most others will do the same. Just be confident, hold your head high and go out and put yourself in situations where you're sharing experiences with the kind of people you want to have as friends.