In my personal experience "ha ha" is an almost default result of trying to avoid "lol." Why I try to avoid lol is a deeper question, but it has to do with AOL and how AOL looked from Compuserve in the early 90's. Anyway, yes I'm old.
Interestingly enough, I use "Haha" to denote sincere laughing. Mischievous laughing goes as "Hehe"; imitating an overweight person goes "Hoho" and normally imitating a timid person (or a woman, and I swear they are not related!) goes as "Hihi."
I use "heh" to denote "I read your message, but I'm busy and I need you to stop talking to me". "I read your message, and I was mildly amused, but not enough to continue talking" is "hah". "I actually thought that was funny, but I'm still busy" is "haha". Real, actual laughter that wants to continue the conversation is "hahaha".
I thought this was a secret code only I knew. Now I have to conjure a different way of subliminally communicating my indisposure to chatty friends.
Also, "hehe" means "only mildly amusing, but I'm not busy so I'll keep talking". (Unless you say "hehe" after something you wrote yourself, in which case it's creepy.)
Likewise, I only use "Haha" for things that are truly funny. "lol" is reserved primarially to lend a degree of self-awareness to a particularly absurd or stupid statement that I say or recieve.
ha
haha
hah
aha
ahaha
'ha ha'
hahaha
HA
HAHAHA
hahahahahahah
haaahaaa
lol
LOL
LMAO
lawl
elohel
'ha, ha'
ha.
heh
hehe
bwahaha
'ha,'
though it's really hard to describe exactly the differences between them.
context: I'm in my twenties and grew up using AIM and FB and playing MMOs. I think those are all relevant to the exact 'vernacular' I've ended up with.
Don't forget "lolololololol", which is different in meaning from all those you listed. (Specifically it is a form of sardonic laughter, as in "did you hear that Trump is running for president again?" "wtf no again?? / lololololol".)
In Japanese, people usually end a statement with "w" as it is short for 笑う (romanized: warau) which means to laugh. It even parallels "lololol" by adding more "w"s (i.e. 偶然だwww).
Korean actually has a generous share of onomatopoeic words: for laugh, there's at least haha, hehe, hoho, heoheo, huhu, and kkalkkal, and that's just counting more or less standardized words that would probably appear in most dictionaries and have well-understood connotations.
Interestingly, Korean internet somehow settled on ㅋㅋ (literally, "k k"): the closest word I can think of is 크크 (keukeu), which is... well, the kind of laugh a villain might make after explaining to a captured hero how he will be thrown into an elaborate death trap.
(And don't believe some internet sources that say Koreans laugh "kekeke". It's simply because the sound I wrote as "eu" ("Close central unrounded vowel", or /ɨ/) has no English counterpart, so people wasn't sure how to write that in English. Besides, nobody's gonna pronounce "keukeukeu" correctly anyway, so why bother.)
"w" in Japanese is not an onomatopoeia but an abbreviation (for 笑い "warai" laugh) as same as in English "lol". There is an actual laughter onomatopoeia in Japanese too, it's "fu(fu)" or "a(ha)".
I know many Korean speakers use "ㅋㅋㅋㅋㅋ" to express laughter. The "ㅋ" symbol has a sort of "kih" or "kuh" sound, so it's meant to represent a snickering "KihKihKihKihKih!"
I can't stand lol either, I recently was taught by my daughter that I was using heh a bit too liberally, and hurt her feelings. In rl its pretty hard to get more than a smirk from me, been using hehe more, correctly or not...
The first paragraph resonated with me a little bit. When I was younger (14-16) I'd always try to type as correctly and "seriously" as possible. I literally thought everyone who didn't do the same was just stupid. My IMing style is pretty much the opposite nowadays. And as much as one hates being biased I have to admit I still judge people on their typing style a bit. It's pretty hard to gauge one's tone/feeling/attitude without having all the hahas, emoticons, smileys, redundant words etc. Do they not like me? Are they trying to be rude? Are they being creepy? Are they just not much of an internet chatter? Is that just an aspie-like trait?
I used "haha" mostly to avoid saying "lol." As crazy as it sounds, I got too lazy to keep doing that. Lol is all wIth one hand, and doesn't denote true laughter. It's more, "I received your message" than anything.
In Thailand, the default is "555" since the word five in Thai is pronounced "ha". Everyone in Thailand knows what it means, and the rest of the world must think we're crazy.
On a side note, my personal favourite is the Bender laugh... "AHEHAEHAEHAHEAHE". It denotes forced amusement with a side of cynicism. And it's brilliant.
'hihi' or 'hi hi' is another, fairly rare, written variant that is used as laughter in morse code, and has migrated to written text by people that commonly use morse code.
I'm not sure the exact reason, but it does make all the letter dits. 'ha' is spelled .... .-, but 'hi' is spelled .... ..
Fifteen years ago, I got temporarily banned from an English-speaking IRC channel (#gamedev on AfterNET) for my part in instigating the ironic usage of "kekeke", which was very well known at the time due to the popularity of Starcraft in South Korea.
It feels weird using "hehe". I type it exactly how I laugh, "haha hahahahahahaha". Although if I feel I might look stupid I try to tone it down with a simple ":D" or the emoji with the laughter to tears.
What a meaningless parade of speculative bullshit. There's a science for discussions like this -- it's called corpus linguistics. There are people who have spent years of their lives trying to understand observed patterns in behavior using real data and statistical analysis. This a handful of anecdotes that even the most generative of armchair linguists would roll their eyes at.
Has the New Yorker ran out of ideas for important issues to cover? It's funny, granted, but with everything going on in Baltimore and Nepal, it seems misplaced or at last badly timed.