I know that そんな means "like that", but as I read more and more mangas, I get the feeling that it is also used as an expression of disbelief. Can someone elaborate and do similar words like こんな or どんな have similar use in this case?
そんな itself means "such" when it's used before a noun or to refer to the amount you are seeing when used as そんなに. So, yes, it can be used as an expression of disbelief.
Are you going to eat that much??? (You see lots of food in front of the person and you can't believe that the person is trying to each that amount of food.)
Did you eat all of them??? (You see lots of empty plates in front of the person and you can't believe that the person ate all of it.)
Don't do such a (stupid/dirty) thing
Don't say such a (stupid/cold/cruel) thing
So, taking @NothingAtAll's advice...
You may hear people say
そんな。。。, which has the nuance of disbelief because you are just not repeating or describing the details (ellipsis of the above examples), and it kind of means like
Oh no... by itself
A: You are the worst student I've ever had
B: そんな。。。 （そんなひどいこと言うのね。。。）
A: You are not allowed to join the party!
Since it's already been answered, I'm just gonna make an example where that particular meaning of そんな could be used.
A: The truth is that I'm not your real father...
And you could imagine the shocked child falling to his/her knees.
That そんな can be translated as: "It cannot be..." or "Impossible..." or "No way...". As I see it, it's close to what Nothing at all commented.