I'll take the Urban Dictionary definitions and try to show you how the words putain, bordel and merde can fit in any of those situations. To me it's more of a matter of how you say the words than a matter of words themselves. Hence my answer is more for spoken French than written French:
Surprise
One might add Oh in front of any of those words and get the "Holy fucking shit they found water on the sun" effect: Oh putain, il y a de l'eau sur le soleil! as well as the "Holy fucking shit the car in front of us is braking" effect. Repeating quickly that same word several times will add emphasis to the feeling of surprise and urgency: Merdemerdemerdemerdemerde
NB: good parents might say Oh lala in front of their kids in the car situation
Exasperation
The most natural thing I say when something exasperates me is some sort of Rhoo putaaain...!. Another way to handle those beautiful words would be to wrap them with mais and quoi, for example Mais merde quoi!. The wonderful Putain de bordel de merde works quite fine here. This is where the word bordel belongs the most
Indignation
Using those words to convey indignation is very similar to exasperation. It will be said in a more energetic way though: Mais putain quoi! C'est pas possible!
Wonder
To express wonder, once again, those words can be used. If you've been hiking for hours and finally reach this beautiful landscape you've been craving for, you might drop a ooh meeeerde! with a big smile on your face.
In short, if you say any of those words with a tone that expresses your feelings, it might just work ;) Thank you for that question, I had never thought of how various usage we have of those words. And there are even more!