Invented language can work, admittedly, it just so often doesn't because it doesn't have the weight behind it as a term the reader knows. I've long criticized invented vernacular for more often being awkward and clunky than it is useful or timeless. Most times, I'd much rather someone just use a real-world phrase or term of strong language, aside from instances where it would be silly (specific religious-based utterances, for example).
That said, I do think that if you do it well, original vernacular can be interesting and add a lot. Or you could even go for real-world mostly and then add in some colorful phrases with specific characters. It doesn't even have to be cursing necessarily, but it can be an utterance of surprise, shock, or the like.
For example, in my previous long-running comic Incubus Tales, the main character Dhiar's favorite exclamation was "Great Gilgamesh's gonads!" It's a vivid sort of evocative utterance (as most strong language, if you think about it, usually is), and it's immediately something most audiences would understand. He didn't say it often -- just when he was particularly surprised. So when he said it, the audience knew something shocking had happened.
Like most cursing and strong language, it referenced a notable character of myth or legend, referenced a typically private or evocative part of the body, and had a nice alliterative quality that made it flow off the tongue easily. I was pretty proud of it, because I feel like it's something that a person would actually say. It was, however, pretty much only the one character who said it, and this is part of what I wanted to convey: people will often have strange personal sayings that they might utter instead of just a plain old curse or profanity, depending on circumstances. This is where that originality can come very much in handy.
Plus, if you want to make it a thing with the story in general, the other people around that character could learn the expression and take to it...just as often happens in real life!
It's worth noting that it doesn't have to be anything like that expression, though. One of my favorite characters in the Doctor Who I grew up with, Tegan, had an expression of exasperation that she had learned from her aunt. What was it? "Rabbits!" It's all in how you say it. You can make even an utterly innocuous (or charming) word sound fierce, if you use it strategically.
