1st: where to use? Doing what and in what way? Design parodies? What audience? Jurisdiction (where are you, the brand and the product) also plays a key role in all of this.
From an entrepreneurs view Its simple: for a limited audience, to make a point, ok. Can be acceptable and the possibility of backfiring is not that much. Worth the risk.
For commercial use, depends if you wanna risk a lawsuit or not. A single lawsuit can ruin a company in a second. Depending on where that company is registered, of course :D
Some of the exemples you mention (brands) are highly susceptible to causing problems. Others (periodic table) are not so much, because they are free knowledge.
I have found out that exact copies cause usually problems. "Blurred" visions, only using core concepts is usually less risky. Even if Mario is not very perceptible if I see a little guy running with "mario colours" my brain will perceive that. I recognise thats not the one, even that you are using it, but just different enough to not get caught. I've seen this example before and it worked.
One thing thats also important is to search the web before, try to understand the behaviour of the their legal department. Finding some cases is also helpful because the rulings will have the "boundaries" written all over.
If they are very active I wouldn't go for it.
If your product depends on other brands to "work", I would strongly advise you to sought a professional before any launch. You don't want to spend a lot of money just to discover you burned it.