It usually has an air of mockery, specifically with regard to teenagers who a lot of use three-letter acronyms.
Computer Nerd #1: I mean, just because it's https doesn't mean it's fucking legit
Computer Nerd #2: Yeah, I'm sure those idiot script kiddies would love to get their hands on a secure server so they could grab some more AOL passwords before they hit up the child pr0n
Non Computer Nerd: OMGWTFBBQ please kill me
Example #2 (def: mockery)
Teenager #1: so i was all like, stacy, if u want a loser like steve for your boyfriend go ahead!!!!
Teenager #2: lol
Teenager #3: omg i can't believe u said that!!
Cynical Generation X-er: OMGWTFBBQ
Partycrashing Smartass - "Omgwtfbbq I r teh l33t dipshittings."
OMG WTF BBQ was made for people to use when they can't stand the acronyms anymore. It's generally understood that once you are BBQ'ed, you must end the acronym talk and speak actual English.
Person 2: "OMG WTF BBQ!"