Q:

Where's the balance between realism and story?

Mark mentioned in his answer that plotholes aren't usually the end of the world, and that I shouldn't sacrifice too much of the story and the characters for the sake of logic.
But there's a breaking point where everyone goes "That makes no sense!"
The other is with an idea of mine: Essentially the parody of the 2003 Clone Wars miniseries by Gendy Tarantino Tartakovsky.
It takes the rule of cool, prevalent in the series, exploits and abridges it when Styropyro, Szertár, Sam O'Nella, and Ms. Frizzle overtake the series. They abuse Grievous with 7W laserpointers and flashbangs, blow Durge up with IEDs and destroy an army of 200+ droids with a blaster, a GoPro, a smartphone and Osu Kissing the Tears levels of jackhammering on the trigger.
There's silly stuff like when G blows up and only his head remains, he says MC (main character) stands taller as a warrior than he does. Nonetheless this idea's essence is  practicality > literally Samurai Jack but with laser swords
One could argue that such moments won't harm the story's overall tone as a funny love letter to those who thought Holdo's driving skills are what ruined SW's worldbuilding.
But what should I do when the story is actually serious and logic is a cornerstone of its premise but it could get in the way of other stuff?

A:

Is there a breaking point where people say, "that makes no sense"? Certainly there is, but I don't think it is anything you can quantify. In fact, it is demonstrable that that point is different for different readers, some condemning works for making no sense while others ignore the contradictions quite happily. Some audiences will quite happily ignore absurdities that others will not tolerate. And that is fine, because no book ever written has ever appealed to the entire world. Every best seller has its detractors. 
Nevertheless, I think there are two very basic things you can do to minimize the risk of people saying that your story makes no sense. 
First, understand the difference between a plot hole and a character inconsistency. Stories are basically about ordinary people in extraordinary situations. It is given to the reader that the situations that occur are going to be unusual, at least. They will forgive a lot in this department. But characters have to be consistent. If you start having one character act or talk in a way that is inconsistent with who you have shown them to be earlier in the book, the reader is going to lose confidence in your story pretty quickly. After all, if the interest in the story lies in how a person of a particular character handles the extraordinary situation they are in, all the tension and interest goes out of the story if they suddenly change character in the middle. So, worry much more about character inconsistencies than about plot holes. 
Second, forcing your characters toward the climax where their character and resolve will be tested and where they will have to make a choice of values may involve creating some pretty unusual situations or events. But there is a simple technique for making the reader accept these situation and events. It is called foreshadowing. Thus if you need a tornado to hit the house at a critical moment, it will seem completely contrived and unbelievable if there has been no mentions of tornadoes previously in the book. But if there have been prior mentions of tornadoes, then the reader accepts that tornadoes are part of the world of the book and does not gape in disbelief when one comes along at just the right moment to force your protagonist to face their moment of crisis. 
Often authors, having contrived some event to force the crisis in their novel, go back and find a way to foreshadowing it earlier in the book. I saw Bernard Cornwell at a conference once explaining that if he had Richard Sharpe escape through a door in chapter 10, he will then go back and have him walk through the same door in chapter 3. This simple foreshadowing is often all it takes to make otherwise unbelievable events and coincidences seem entirely plausible. 

A:

If I understand your question correctly, you're asking to which extent the Rule of Cool trope would let you get away with things in a relatively realistic story.
The answer to that is, distinct story elements have to match the overall tone of the story. Otherwise, they stick out like a sore thumb. If an element "doesn't fit", then you can't insert it. No matter how much you might want to.
You do get some leeway. For example, a story element might be hinged on contrived coincidence. It could happen, it's just unlikely. Consider, for instance, Victor Hugo's novel Les Misérables: in all of Paris, Marius just happened to rent a room next to the Thénardiers, with Marius's father believing his life had been saved by Monsieur Thénardier. And Marius is in love with Cosette, who had been a ward of the Thénardiers. Not very likely, is it? But the story can hardly be considered unrealistic. In fact, it's power is derived from the fact that readers felt this could happen, this was happening all around them.
You also get away with inherent illogic of core story elements, without which there is no story in the first place. For example, Tolkien's legendariun is not a pastiche or a travesty, it's not a humorous work, it doesn't suffer from lapses in logic. But it contains dragons, and immortal elves. Tolkien doesn't have to answer how dragons breath fire, how they fly, how comes elves don't get old - those are axioms, on which everything else is built.
A simple rule of thumb: if something feels to you like it doesn't make any sense, don't write it. If you can't make yourself believe in a story element, there's definitely something wrong there. If something makes sense to you, but not to your beta readers, address it - either provide the story framework for the element to make sense (as @Mark Baker points out: mention tornadoes, so the appearance of one isn't "out of the blue"), or change the story element. If it took for your work to get printed before someone spotted an inconsistency - you got away with it, but try to do better next time.

A:

The technical name for what you're describing is a "travesty." Often mistaken for parody, the travesty is a thinly disguised version of someone else's work, used as a setting for cheap gags. The difference between a parody and a travesty is that a parody is capable of standing on its own, even if you don't know the source material, whereas a travesty draws 100% of its strengths from its source or sources. It doesn't have any internal coherence or logic of its own. Travesties can be very popular, but no one would ever consider them great art. This is not what @Mark Baker is talking about. 
The core idea is that stories are not reality, and we don't expect them to be.  We do expect that settings will have their own internal logic and coherence, but readers will overlook minor flaws in that department if the story is strong enough, and if it makes emotional sense. We do also expect that the author will not unnecessarily endanger our suspension of disbelief.
For these reasons, cheap gags don't generally belong in a story that you want to be taken seriously.  You're probably better off trying to mine the intrinsic humor that is often present under the surface in serious situations. It IS possible to take a concept that sounds trivial on the surface, and endow it with real weight and meaning, but it's not easy. The comic strip 1/0 started out as a cheap travesty on webcomics, and ended up as a substantive meditation on life, love, religion and the nature of existence, but that's definitely the exception to the rule.  Murakami and Pratchett have also had success in bringing real weight and heft to concepts that seem impossible to take seriously --but they're idiosyncratic geniuses.  If you're working at that level, more power to you.

