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The laws on this topic vary from country to country. But I can answer for the United States.
First, you are free to refer to other works by their title (e.g., songs, movies, plays, novels, etc.). But you are not allowed to include material from those works without permission. For example, you can have a character say their favorite Broadway show is The Producers, but you can't have them break out into a musical number from it. Similarly, a character can make an allusion to a Stephen King novel, but you can't have them quoting it without Mr. King's prior approval.
Second, in general, you can make references to any famous person you like without fear of reprisal as long as you don't do so in a negative manner. Speaking about a person neutrally or positively leaves no risk of defamation. However, if you're concerned that you've written something that might qualify as libel but you aren't sure, then I would suggest posting a new question regarding that specific instance, as there's a lot of nuances to consider that go beyond the scope of this question.
Now, when it comes to naming your characters after other fictional characters, there's broadly two angles to consider. Names themselves aren't copyrightable unless a) they're unique to a particular work, or b) the name also appears in association with a unique creative expression or attribute which together form a copyrightable entity.
It's easiest to explain with examples:
Obviously, everyday names like Bob or Luke or David pose no issue because they don't necessarily call to mind any specific character. However, you cannot have that same Luke character go around swinging a laser sword, because "Luke + laser sword" does evoke a particular copyrighted character. Even if your character is wildly different from Luke Skywalker in just about every other way, it would likely still constitute infringement.
Naming a character MasterBlaster could be seen as copyright infringement, since there's no question that MasterBlaster refers to a specific character protected elsewhere by copyright. If you want to play it safe I would recommend you avoid using such a specific name directly.
The situation is similar for a character nicknamed Mouth, especially if they largely resemble the original Mouth. Unlike with MasterBlaster, there's more gray area in this case insofar as "Mouth" is such a general, common word that doesn't necessarily bring to mind the Goonies character every time you hear it. But, the character Mouth is a protected artistic expression, so personally I would be hesitant to use it in this context (especially if your character does indeed behave a lot like the original).
However, if you want to make a passing reference to the original MasterBlaster or Mouth in comparison, that's usually fine and constitutes Fair Use. For instance, one character can say, "Dude, you're whinier than Luke Skywalker!" This is OK as long as you don't do it repeatedly for the same reference.
Finally, it should be said for the sake of completeness, that none of this matters if the work is already in the public domain. But little to none of the material you would likely be concerned with from the 1980's will likely be in the public domain yet.
An alternative approach:
If there's some pop culture item in particular that you need to touch on often throughout the story, one technique is to invent a slightly modified version that strongly resembles the original but has some tiny differences. This is not a copyright violation. The audience would understand the connection, so the effect is essentially the same. This also has another potential benefit in that your readers might be favorably amused by your twist on the original, making it memorable in its own right.