It's important to realize that there are two dimensions at play here. One is the "heartfelt" dimension, and the other is the "formality" dimension.
Both ありがとう and どうもありがとう are casual in the sense that you should only use them with people that you do not use 丁寧語 with. どうもありがとう shows more sincerity than ありがとう, but even (本当に)どうもありがとう would not be appropriate to, say, your boss.
ありがとうございます and どうもありがとうございます are for people that you use 丁寧語 with. Again the version with どうも is more heartfelt. Some people might feel that it is also more formal, but I would say that is merely because very formal situations often call for exaggerated words of sincerity. You would not use ありがとうございます with, say, a close friend who you do not use 丁寧語 with, no matter how grateful you are, except maybe for comic effect.
As for どうも by itself, the situation is a bit complicated. You will often hear どうも used in situations where the speaker would use 丁寧語, but depending on the formality of the situation, it might be seen as a bit curt. Note, though, that it would be a different reaction from the one that one might get using ありがとう which might be seen as downright disrespectful.