It's normal here to show up with un-invited guests and it is also normal to order expensive things when invited for dinner.

tell them the invitation is only for them, no exceptions.  If they can't come without their BF/GF/BFF, too bad.  The strictness will help limit the numbers.

This is a gesture to be nice, purely for class comradery, not to be taken advantage of, I'd tell them that.  Who cares if it follows usual Chinese procedure, it's your dinner, not theirs.

Tell them clearly about you will pay all the bill, but you cant afford to pay their gf/bf etc whom are not in your class. I don't think your students are all that stupid. Just make sure them UNDERSTOOD what you want to do with them, what you dont want to do with them!

Definitely tell them if they insist that they cannot come witout their rommates best friend, etc. that "sorry to hear that, you will be missed".
I had a similar problem and on many ocassions, the boy who was not allowed to come without his girfriend would often show  up anyway, without her!

Just to follow up, the cost isn't even the main factor. I respect the class because they are learning international law in English, many struggled the first month but through hard work and extra classes pulled through.

I've become good friends with many. The point is, at the dinner/event whatever, I want people to have fun, talk about some in class jokes [such and such loves such and such] and relax. Although I can talk Chinese, I also would prefer that they continue to talk about things that we did in class, and many have wanted to talk 'other topics' but I told them that I could only do so outside of official class.

That and I will be giving out some small christmas prizes and presents, and I can see now that all those with bfs/gfs will be far more reserved and quiet infront of their other halves, or just spend the entire time talking to their bf/bff/gf.

Or ask you "Why didn't my FB/GF get a present.....?"

your first mistake thinking you're in civilized society with people who have manners and have a sense of decencey. in our countries no one would bring their gf/bf unless the invite was plus one even if the invitee was a millionaire. but here they think of all foreigners as ecessivly wealthy
second dont think it's a cultural gaff on your part your students are looking to take advantage of you. pay the piper now and be sure never to make that mistake again. 

scout the restaurant and find one that is good and cheap and then take control of the menu and do all the ordering . do not ask them to order anything. under order on purpose because some locals like to order everything on the menu when someone else is paying 

this kind of thing really pisses me off....
As someone already mentioned, tell them clearly that they cannot bring partners and if that means that the student cannot make it, then so be it.

Im telling you, they WILL be showing up without their partners. When was the last time you saw a Chinese person refuse a free meal!!!

Make sure you are clear that only your students are invited, not their significant others, this is for your students only. Also, you should take over the ordering and not ask the students to order. When we go out to dinner with our Chinese friends and they treat they do all the ordering. You can ask them to make suggestions, but make sure that the waiter/waitress knows you're the one in charge and doing all the ordering and paying. They will come to you directly everytime if they know you're the one with the money.

four or five said 'I can pay for my girlfriend' but then I can see the scene now. I divide bill and pay for students then one boy says 'my girlfriend doesnt eat meat and didn't drink beer'. it'll degrade soon

also WHY do people take advantage? they should know in the west if invited out and someone is paying I will generally look at the lower end. last time fair enough I was cheersing so many beers were drank but two fish dishes were 45 and 65 each and tiny. also they ordered the large plate of meat with gloves provided for 60 x 3. so that's 280 for three dishes. I guess taking advantage is in their nature. needless to say when they invite me I will order a 200 KUAI fish dish and then not eat it. muhahaha.

Once upon a time...That's how most stories begin.

 met a girl, skinny, little but overall not bad looking. Was talking with her and she told that she only made 1200 a month and never had eaten western food. (we were talking about western culture btw.) and that she would like to eat pizza. I told her that i would invite her one day to go eating a pizza in "pizza hut". Well next appointment was in the pizza hut ( I thought we are ging to eat just a big pizza). She asked what to choose. I told her in my country everything you order you also need to finish, otherwise it is not polite. (different then here in China). Anyway she was skinny and i thought she would be full with a pizza. Well..... I ended up with a bill over 700 yuan though. Never have seen such a skinny person eating so much. (never invited other either). For ending this story, I also didn't got laid as she needed to go home and didn't felt very well because she eated too much. WTF.......Pfffffft............

I regularily have my friends or even my gf who I have invited out show up with random people to get a free dinner.
Problem is I am too nice sometimes, but I gave my gf crap last time she pulled this.
It is ok if they ask, but to show up with a stranger is just not cool, especially when they want to help ordering.
And judging from this post and answers this is obviously a widepread issue....but would they do this to locals that invite them out?  Or this just a loawai thing?

BTY...I agree with everyone who said tell them no to guests...thats my 2 cents.

I think you blew it by mentioning "KTV".   It would have been all fine, without it.