I was in a similar situation when I first came to my school.

I carry a stick, like all the teachers here, but that doesn't mean you have to "beat" students. I use mine for pointing at the screen or chalkboard, and for banging loudly on the desk to get attention.

So if you don't want to hit students, that's just fine. But you have to control them somehow. Personally, I use the threat of the stick-- but when it comes down to it I discipline in other ways, which are also seen as "corporal punishment" I guess. Such as making them raise their hands over their heads, or pushups. Sometimes I [mod edit: tell the student to go out to] the hall. Sometimes I draw a picture they do not want on their face in permanent marker.

The students are used to the discipline here, and if you try to apply western discipline in the classroom you will likely be ignored (unless you are already respected/feared). You can try it, but it didn't work for me.

My biggest asset is the support of the other teachers. I have the power to permanently remove students from my class, and I will remind them of that if they are continuously bad. They do not want this, because my class is much more fun than a regular class, so they should straighten up a little. If you can do this, do a 3 strikes policy then boot them out. Don't fall for any second chance stuff.

I have permanently removed students from my class on the first day before. There is a long enough waiting list where the spot can easily be filled. The students get into my class by competing in a rock paper scissors tournament, so there is no filtering of bad students during the "selection" process.

Once you've secured a little respect (or fear?) you can start to build on it. My after school & before school class is my favorite part of the day. It is quite relaxed and fun.

I teach at a Middle School Boys school with 1000 students (G1,2,&3). I see students once a week a week and was basically told not to teach from the book. I also teach 8 hours of after school each week (just like your situation, also without a book). Here are some tips that worked for me (for after school):

Being Prepared- If you don't put in the effort, you are guaranteed to fail!

Seating-make sure you have less groups to control (example: 24 students=4 groups of six (not ideal for conversation but much easier to control than 6 groups of 4, make seating charts if necessary, also helpful if there are very low students, just put a high student next to him so they can help teach-most of the time they are not paying attention because they don't understand.

Structure-Make the last portion/period of your class a game, if they finish early more game time, or if bad no game+extra worksheet (example: I bought english games like monopoly, scrabble, boggle, and pictionary: I teach 2 sets of students 4 hours each, the last hour is game time (in english of couse, after they got used to the games I had each group present (teach) a game to the class in english). I know I also try harder if I have something to look forward too!

Material/Lesson- It's ok to have fun. When I first started I took everything too seriously. I didn't take into account that these students go to school 12 hrs per day and may go to your class because their parents make tem...or can't afford hogwons. Do what you cant to motivate the students by making the material interesting, then using that interesting material to create activities that get them learning and speaking (waht they might call "fun"). Hopefully you both will have more fun. I learned the hard way teaching more isn't always the best approach. Mix it up, have fun, it something isn't working then try something new.

Classroom management-If the advice above is working then this will go a lot easier. These students are here becuase there parents make them or because they want to be. Being [mod edit: strict] may work for some, but showing that you are conrcened about their education works for me. Give them minus points points, if that doesn't work then have them go to the back of ther room, not let them participate in games. If they are the "problem student" just tell a korean teacherl, problem solved!

Reward-make a group point system, winning group gets candy. Sometimes hust the competition is enough... Also maybe points build up to a movie (also less work for you, and you have a good reason)

Always make sure to put yourself in thier shoes.Odds are if you are not having fun teaching it, the students are not having fun! Granted, all classes don't be fun. 
I have only been teaching for 9 months, I do not claim to be the best teacher. I give my best, and that is the best I can do. Don't expect to work miracles so when they don't happen you won't be too disapointed. These are only my experiences, take only what you think might work for you...

I have a difficult time some times and my co-teachers are useless in helping. Here are some of the tips I would do:

1) Write down what LivinginUlsan suggested as it is sound advice.
2) make a PPT with rules (with Korean) for the classroom and/or get them to help you.
3) Get some rewards and change it up a bit.( I had an extra cup-ramyon one day and it was the best class I have ever taught because they were all trying to win the prize).
4) Groups are great, but have a floating seating plan. If they are talking, move them. I also make use of what I call the "Hot Seat" where I site a student in the front of my class and direct all the questions on to them.
5) Be Positive. It sounds stupid but if you smile and are excited to do whatever (even just make a joke about things) they will change their attitudes.
6) Competition! These are boys and they will step over their own dead grandmother if they can win something. Also, have a funny prize for the losers so they know that they have to try and do something. I have the losers do a chicken dance.

That is about it. I have included the rules that I started with my first graders. You may want to try these out. I may suggest "starting over with them" and see what they want and then use this as "what you want"
5)

If your kids are anything like mine ( I also work in a low income area) they wont even hear you trying to organize them into seats. You will get one group situated and the ones behind you will have ripped the speakers out of the wall (yes this has happened to me). And these are 1-2 graders. I feel your pain.

One thing that works for me and I don't know how this works but it does ...occasionally... so you don't scream yourself horse trying to be heard over the roar....anyway usually the good kids sit in the front right, they want to learn. So when the bad ones act up I just give them the stare (Korean kids don't liked to be embarrassed so staring at them in a disappointed manner will make them lose face a little), say be quiet a few times and do the shush symbol (index over lips) for as long as it takes for the good kids to get annoyed that they are not learning and get the bad ones to be quiet. This only works if there are enough good ones.

If it gets really bad you can always call another teacher from next door to shout at them in Korean as you point out the perpetrators. They will lose face with other teachers here too and they wont like it. Depends on your relationship with the other teachers.

Sending kids out of class works. If someone asks them why they are out of class or if have to go back to their homeroom teacher and they have to explain they were kicked out this wont look good for them either.

I know a lot of this has to do with shaming kids into behaving better but if you can't hit them and disciplining them is difficult if they wont listen to you then the only thing left is to try to get under their skin  a little.

A lot of these kids are acting out because they hate where they have to live and go to school. Don't yell it only gets worse. Try to befriend the worst of them I know it seems hard because you want to strangle them lol but if you curry favor with them they will be better for you. Most of the time they just want attention give it to them out of class and inside of class they will love you.

Good luck!

Last method is removal or expulsion from the class.  They have no concept of suspension here in korea (unless you like, assault a teacher) and instead rely entirely on physical or emotional means of enforcing authority. 

I however, have found that removing the ring leaders from class all together not only removes the problem, but it also emphasizes to your co-teachers that you simply can't handle those kids.  and the truth is you can't.  you don't understand their language and you aren't willing to play their games to enforce discipline (i'm not willing to whack a kid either).  so.  removal is really the last best option.  talk to them after school with a teacher about why they were removed and howthey will be removed again if they are bad again.  If you can get one of the really good disciplinary teachers to help you with this it can be super effective.  I had some pretty bad students students turn around and actually be little sunshines (still not good at english, which is the real problem, but at least attentive).  I'm talking punks with earrings, smell like smoke, often skip school (so i hear).  And then there's one who's reeeeeeal bad but basically he just stays quiet now (which is exactly what i wanted).

It's hard to know who to target for these if the whole class is rowdy so if it's real bad I'll just do a sweep of people i assume to be ringleaders. 

again, this is like, THE last resort.  otherwise go with livinginulsan and whatnot.  that's your standard means of control.

I should point out that I'm basically in the worst teaching district in all of seoul.  everyone thinks they work at a poor/sub average school but we are statistically one of the worst, apparently, with all the behavior problems that come with it.  I rarely have to yell anymore though. 

"Sometimes I draw a picture they do not want on their face in permanent marker."  haha I like this one.

One more thing, you will have good classes go wrong for reasons beyond your control or understanding and bad classes that will continually surprise you in their ability to improve.  Its important to start each class with a clean slate, try to believe they can be great and they will occasionally impress you, when they aren't driving you crazy.

Sometimes you can lose the last 15 minutes of any class (its not you or your teaching), and its best to not take it personally when you have to punish them, be willing to do it.

A active co-teacher can make a huge improvement, but that's largely beyond your control because you are a junior temporary teacher.

3)On punishment: Leave it up to the co-teacher. Taking the discipline into your own hands only backfires. The kids won't listen to you and the co-teacher will feel out of place. If they won't be quite or listen, simply refuse to speak until they do. Request their silence and when they don't listen just tell them you're waiting. Sometimes I'll even pull a chair to the front of class and sit down. It surprises them and its also a wake-up to the co-teacher that he/she should be doing their job.

This may vary depending on your co-teacher. I've had one co-teacher go off at me for letting them be loud and that she had to do it, rather than me.

Yellow card and red card penalty, like soccer.   Yellow card they have to stand up until you think they behaved well enough. If they still misbehave then red card. Red card the go outside or have to go to back of the class and stay in a push up position.

Ugh.  Good luck. Korean middle schoolers, especially the older kids, are terrible.   I just the worst class ever - coming down with a cold, it was my worst-behaved class, and my co-teacher was gone all hour disciplining some other kid.  To make matters worse, before she left she told the whole class "be nice to your teacher, she is sick," which backfired as these monsters lack any faculty for empathy whatsoever, and all they heard was "she's too weak to control us!  let's party!"   

I am counting down the days until my worst class graduates and I no longer have to see their faces in my room ever again.  They're gone soon, which is part of the problem of course - they're basically done and just counting down the clock themselves, so they have no incentive to learn anything.  Especially difficult subjects like English.  just keep the lessons simple and easy enough for them to do, and mix in games and Mr. Bean every now and then (although today with my worst class, I erased the game from the lesson plan because I felt they did not deserve it.  bah).