I agree with YummyMummy that you need to contact the people who have added to their invites. It's very rude, as a guest, to invite extra people to someone else's event.
I personally would not mention that other people have done the same - (I can see that turning into an excuse for them to say you're being unreasonable, it's normal to add extras, look everyone does it...)
Stick to "I'm afraid you've misunderstood. The invitation was for John and Jane . If we had been able to invite Janette and Jonathan and little Sproglet we would have sent them an invitation / put their names on the invitation. We have a very strict limit on the number of guest we can invite and we are not able to add to it in any circumstances."
If they push, I would move on to
"I hope you, John, and Jane, can still attend. Please make sure that Janette and Jonathan understand the situation, that while we would have liked to be able to invite them, it just is not possible. Please don't encourage them to come, as it will be really embarrassing for them to be turned them away,and I'm sure you would not want to be the cause of that"
If you think the original invitees won't accept what you say then I would contact the extras direct and explain that unfortunately, their has been a misunderstanding by their parents / siblings (whoever is adding them on) and that you just want to make sure that they know that while you'd have loved to be able to invite them, unfortunately the limits on the size of the guest list meant that that wasn't possible, and you don't want them to be embarrassed by being turned away as a result of their parent/friend/whoever's misunderstanding. It's an awkward conversation to have, but better to have it in advance, when you can make clear that you have just found out about this misunderstanding, than to find you have uninvited guests showing up at the wedding.