Q:

Questions about meanings and usage of "deez nuts"

Please note, I did check the Urban Dictionary, and also Stack Exchange.

What was meant by the OP in https://english.stackexchange.com/questions/268152/what-is-the-origin-of-best-boyfriend-ever 

“What can I say but :/ omg deez nuts.”

What is meant by "Deez nuts ain't loyal"?

Edit 8/28:
The bounty is helping, thanks to all for contributions so far.
is used as a ribald non-sequitur -- that is how it has been used by my pre-teen son.  Since he has echolalia (a symptom of Tourette Syndrome), there are a number of words and phrases he repeats that have no particular meaning.  Ribald I already knew.  I also knew my son uses the phrase as a non sequitur.  Is it a non sequitur for others, too?
I'd like to understand under what circumstances people say or write it, and what message or tone or something they are expressing when they say it.  I'm sorry if this is obvious to others.

More progress (8/30): Q1 -- It turns out that the OP was just writing a list of annoying modern slang expressions, so that thread is not going to help me understand under what circumstances the phrase is used, and what it is intended to express.
Maybe this will help folks understand the question: I've never seen or heard a conversation that included someone saying "These testicles", so just reminding me that that's what "deez nuts" represents doesn't answer the question.
I think it would help to read some sample situations with annotated dialogue containing "Deez nuts".  Anyone?
Or do I need to write a new question?
-- Edit upon awarding the bounty --
I still don't understand it, but now I see that there is nothing to understand.  Sigh.  Thanks, everyone.

A:

1) It's a parody of shallow internet comments, combining several trendy phrases in a manner meant to be reminiscent of an annoying teenager.  In order they are a wry-faced emoticon, an lolspeak abbreviation for the phrase "Oh my God!" and a reference to a popular juvenile joke, where the phrase "deez nuts," meaning "these (my) testicles" is used as a ribald non-sequitur.
2) Although literally a boast of non-fidelity, the phrase originates, as indicated by Alex, as a mash-up of a popular phrase used in several hip hop songs ("these hos ain't loyal") with the joke.
As discussed here, the phrase was originally used as the punchline to a joke where the goal was to trick the victim into providing the set-up (ex: "Did you hear that CD?"  "What CD?"  "See deez nuts!") However, the recent return to popularity was probably as a result of this set of videos, where the phrase is used more as a non sequitur in ambush comedy. http://www.youtube.com/watch?v=VcnUTyI9iJU

A:

"deez nuts" is an extremely well-known slang "meme" in the US, for some 10 (?) years.  It's so well-known I can't be bothered googling to copy and paste information on it.
It has particularly flared up recently and is, one could say, one of the biggest "language meme" stories in the US recently...

http://www.cbsnews.com/news/deez-nuts-is-running-for-president/
Note that the reason the question was asked here, was, someone used
"deez nuts"
and indeed
"omg"
and indeed the emoticon
" :/ "
in passing, and bitterly, as examples of "annoying current slang-and-typographic forms", in the question here.

In answer to your other question,

What is meant by "Deez nuts ain't loyal"?

As far as I know, it simply and rather sadly means "I am not faithful," i.e., I am not sexually faithful, I am not monogamous. Note that "deez" is a rap/whatever version of "these".  (Not unlike "dat" for "that.")

Regarding your now third further, separate, question.  You've hit the nail on the head, "Deez Nuts" is mostly just used as a more or less content-free, silly sort of non-sequitor.  It's just a silly phrase, with silly use. You're not going to "find out" much about the usage of it. It's little different from yelling out "F--- me!" or "F--- you!" in various contexts. That's all there is to it.

