As I understand it, the memes used in the fansubbed version of Steins;Gate were adapted for English audience. The Japanese audience would not know the "Yo Dawg" meme, for instance, since it is an English based meme. They would have their own set of memes, which they could have used in the original dialogue. Of course, it could be that their lines weren't memes at all.
What are the original Japanese memes that were mentioned throughout the series, if there are any, and what's their context?
Some of the phrases are explained at the Steins;Gate wiki's Real-Life References and Glossary.
Regarding the phrase「エル・プサイ・コングルゥ」(El Psy Congroo), according to Anime News Network, FutureGadgetLab is the anime's official Twitter account. According to a tweet by FutureGadgetLab, Okabe Rintarou (lab member #1) explains it as 「お前の胸の中にあるもの。それが答えだ。俺の中ではKONGROOが正しい。『俺の中では』な。《001》」, which you could translate as "It's something that's in your heart. That's my answer. When it's inside me, KONGROO is right. 'When it's inside myself,' y'know." So either the author is being intentionally obtuse (i.e., writing in character), or there is not a specific meaning for it, or the author of the tweet (whoever at the company was assigned to manage the Twitter feed by posting as the various lab members) didn't know what the meaning is. next_tales's answer given at Yahoo Japan's 知恵袋 (chiebukuro, bag full of wisdom) website also says that there is a notation stating that the phrase has no meaning in the 『ＳＴＥＩＮＳ；ＧＡＴＥ─シュタインズゲート─ 円環連鎖のウロボロス』 (Closed Chain of Ouroboros) novel. It does not seem like Japanese fans know the meaning and it is not a general meme in Japanese society. According to the ネット王子 (Netto Ouji, Net Prince) website, the phrase has no meaning but as a result of its use in this series, it has become an internet meme used by Japanese people in their online communications. So to boil that all down, 「エル・プサイ・コングルゥ」 wasn't a preexisting meme used by Steins;Gate, but it became a real meme as a result of Steins;Gate. (Though it is not a meme, the use of Dr. Pepper in Steins;Gate likewise pushed the soda into popularity in Japan [I can actually find it in a vending machine here in Hokkaido now, all thanks to Hououin Kyouma, but see these links: 1 2 3]).
I'd love to hear further answers to this thread's question.
There's references to 2chan if I remember correctly, which weirdly enough they just called image boards in the dub instead of 4chan as you'd expect. Also there were tons of cross culture references to star wars and other movies. Also memes (is it really?) of "all your base belong to us" which I don't know if it is a Japanese meme as well.
I can answer this particular meme.
Fansub: "Yo, I heard you like fail, so we put some fail in your fail, so you can facepalm while you facepalm."
Original: "Dame da koitsu, hayaku nantoka shinai to"
..which translates to something along the lines of "This guy is hopeless, I have to do something about him quickly."
This is a reference to the 2006 anime Death Note.
Specifically from episode 12 around half way into the episode. This saying turned into a meme back in those days, just like the "Keikaku means plan" thing did in the English speaking world.
Concerning 'El Psy Kongroo', while its meaning hasn't been clarified in the anime or by the production team, I think it probably originated from the Danish phrase 'pest eller kolera', which means 'a choice between two undesirable options'. Recall that in the anime, Okabe Rintarou had to make a choice between the α and the β worldlines, a choice between letting one of Mayuri or Christina dies. The writers of the anime probably remembered the Danish phrase, replaced each word by a Greek/Latin sounding one, and rearranged the word order from PEK to EPK to obtain 'El Psy Kongroo'.
