If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?
I think you are most confused about what is meant by “defined in terms of strictly increasing transformations” or being “informationally equivalent. 

You should think it in the following way, a utility function represents someone’s preferences if the function gives a higher/lower/equal value from bundle a than from bundle b if that person prefers more/less/the same bundle a than bundle b. Suppose that such function is $u(x)$, then you can ask, is there a unique function with such properties (I.e. that represents the person’s preferences) and the answer is NO. Any strictly increasing monotonic transformation of $u(x)$, say $f(u(x))$ is also a function describing the preferences of the person. Hence we say that these two are valid representations, and are equivalent (or informationally equivalent). 

Note that whenever you are comparing two bundles you can use any one of the possible representations, and the “strictly increasing monotonic transformation” part is just to check if two functions are equivalent representations of preferences.