それはまるで劇か映画のワンシーン……。
「でも現実の方が意外と奇なり、だったりするのよねえ。ね？」
The character is commenting on the latest event. Without going too much into details, a monster appeared on Tokyo. So she points out that it's a scene similar to a drama or whatever.
Then she adds what I can guess "But reality is unexpectedly more weird, don't you think?"
What I'm curious is what is this construct here? なり、だったりする
なり、だったりする isn't really a single construct. Rather, you're really asking about two different things, so I'll address them separately below.
First, なり is a classical Japanese auxiliary verb that functioned as a copula, meaning that it was roughly equivalent to modern だ、である、or です. As naruto explains in this answer to another question, it isn't ordinarily used in modern Japanese, but it occasionally turns up in particular set phrases. Because なり is obsolete, its use in such phrases gives them a tone that feels formal or literary, and maybe even a little stiff or pompous.
One quite common phrase in which なり occurs is 事実は小説よりも奇なり, or "truth is stranger than fiction." In the passage you're asking about, the speaker is clearly playing off of this well-known expression.
As for だったりする, a special, colloquial usage of that phrase has been addressed in at least two previous answers, by naruto here and by user40323 here. But in this case, I think it's likelier that the more usual meaning of "sometimes" is intended, perhaps with an added nuance of surprise. (The fact that たり can have such a nuance is discussed on page 5-6 of the paper linked to in naruto's answer; if present here, it would reinforce the speaker's explicit use of 意外と).
Either way, it's clear that the speaker is surprised to find herself in a situation in which this cliché turns out to be true. So one possible translation might be
But sometimes, reality really is even stranger than fiction, right? Right?
