Questions about meanings and usage of "deez nuts"
Solution 1:
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
Solution 2:
"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.
Solution 3:
- Does not have an answer, the author likely misinterpreted the meme's usage
- Deez Nuts ain't loyal is a variation on "These hoes ain't loyal" EXPLICIT LANGUAGE WARNING, a line in a song by Chris Brown. Many people said "Deez" instead of "These", so a "Deez Nuts" Joke was inevitable.