Obscure is used to describe things not widely known or understood, such as an obscure literary reference (a reference that does not land well because nobody gets it). Arcane is used to describe things that are known by very few, perhaps intentionally, such as secret or guarded knowledge. You might hear arcane used to describe knowledge of the metaphysical or occult, or to describe rules or information that is so highly technical, most people don’t bother to learn it.
If you have clout, you have strong influence or sway over something. This noun has a long history of being used to describe political influence—and indeed, clout is still most frequently found in discussion of people or entities that are able to drive outcomes in governmental matters. But clout is also used to discuss economic power. You may even find clout used to refer to the influence of a person on social media with oodles of attentive followers.
When it comes to meanings of words, there’s denotation, which is a word’s explicit or direct meaning, and there’s connotation, a word’s associated or implicit meaning. For example, the word frugal on its surface means (denotes) efficient money management (nothing wrong with that!). The connotation of this word, however, might be stinginess or even avariciousness. As any synonym seeker knows, the connotation of a word varies greatly depending on context!